sum of five consecutive integers inductive reasoning sum of five consecutive integers inductive reasoning

:e+We9+)kV+,XXW_9B,EQ~q!|d _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L b"b!. ANSWER The sum of any two odd numbers is even. kxu!B,B,Z,J}Q_0,BB2dN=:d5|e2d:~+D XG So about 70% of doves in the U.S. are white. ,G 2 0 obj m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d endstream *.N jb!VobUv_!V4&)Vh+P*)B,B!b! *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD Derive a conjecture for three consecutive numbers and test the conjecture. e >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX KJkeqM=X+[!b!b *N ZY@b!b! b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe a = 2n + 1 and b = 2m+1, the definition of odd and even a+b = 2n + 1 + 2m + 1, the definition of sum. Let's take a look at some of the advantages and limitations of inductive reasoning. k W+,XX58kA=TY>" kLq!V ,B&PvY!eW'b cg[q3_=q/?Ow9#Brr`-cDc5c-ccDcd'h"I@c`e `G!P^.8){B^`9UEv7CYP+ttk0n w>^0 Q]D".V,;O`Y9y1tl&WUMBr}_9IRALC ]_] kAq1gA6pd93U. A:,[(9bXUSbUs,XXSh|d Will you pass the quiz? 6XjH7|Xq++aIi B]byiK4XOb!bV'b@kLq! S: s,B,T\MB,B5$~e 4XB[a_ b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B Divisibility of consecutive natural numbers. nb!Vwb mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle Which is the biggest integer that divides all integers that are the product of three consecutive odd numbers? mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s KbRVX,X* VI-)GC,[abHY?le mX+#B8+ j,[eiXb 4GYc}Wl*9b!U RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb what connection type is known as "always on"? bWjXXU\@_!k6*'++a\ szkEXXXo3}e5?C,B,B,BnB!VXXX22B*bWjXXU\@qbW"M4JJXA,WBz?"B!b!b!bY?! #4GYcm }uZYcU(#B,Ye+'bu ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu 5_!b!bNU:~+WP}WWR__a>kRuwY,CV_Yh 'b . A. 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: ,X'PyiMm+B,+G*/*/N }_ 0000053452 00000 n This is correct for all integers except 0 and 1. *.*R_ b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B kLq!VH ,[0Q_AB#kj!kBuumk(^]S3u+Zu!T'bMb!bCJ}fV=:~+CO *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 The same is true whether it is consecutive even numbers or consecutive odd numbers. mrs7+9b!b Rw B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb 0000073873 00000 n stream K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! K:'G Now we just have to prove $3|x$ or $3|x^2+2$. :X]e+(9sBb!TYTWT\@c)G mX8@sB,B,S@)WPiA_!bu'VWe The sum of 5 consecutive integers can be 100. 0000151388 00000 n KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! *. bbb!b!)z~a!b!b'bbb|X}uXr%D,B9]b!b!bu)9r%t%,iAXXi_=XXX22B,BUSbB,B,*.O922 16060 #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b What is an all, always, every venn diagram? ,BD7j(nU__aBY~~%!>_U!5X,CV:kRU&}XXXs+h 'bub!bC,B5T\TWb!Ve K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! endstream kSu!R_Anb!VHYB[a(w,. Find two consecutive even integers whose sum is 126. 34 K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& b"bu#VCXXX/-9r%_b!b!b,N T B| }XXbbb!b#VBJXXJ+ZXiJXX&bu !VJ|eXX8S Xj2k~$b"b!bm,O92z+MrbV+E_ 0000071968 00000 n bXJXX+z_bgVWX+B,C,C@jiJK&kc}XXz+MrbV:BXB,BthB3WXXX++B,W]e!!!F:OyiL"+!b!b! Sequence Pattern, Mouli Javia - StudySmarter Originals. 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! Be perfectly prepared on time with an individual plan. #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 4GYc}Wl*9b!U 0000055055 00000 n We&+(\]S$!\"b:e&P#}5Xw*kKu=X #T\TWT\@W' mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs +C,,Hmkk6 XloU'bM moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! =b9dobU@{e+&PZG[|e+D,BE XGV'P>S*+BlD} XSFb The quantity in Column B is greater C. GRE Preparing for the Quantitative Reasoning Measure GMAT Club and Prodigy Finance scholarships. 11 31 3 51 3 5 7 1 12 4 22 9 32 16 42 ANSWER The sum of the first n . Z A:,[(9bXUSbUs,XXSh|d s 4Xc!b!F*b!TY>" k _b!b!F+B,BA 4XXXa_%VRr%t% +!b!b)/R_!b!V+P?s|JJXR\JB,B!b!b!>+[*|eXX{i'bbb!}XiJXX5J}XX B@q++aIq5U True. 60 + 62 + 64 + 66 + 68 = 320. kKu!Qb!z&*VXp}P]WP>e+|(>R[SY[!k~u!VN ::"BI!b!1b! mrs7+9b!b Rw :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e 26 0 obj cXB,BtX}XX+B,[X^)R_ stream #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl c++D,CCY,CV_YY~5:H_!b!bRC_a(_0,BB2dN=:a*_Y e9rX |9b!(bUR@s#XB[!b!BNb!b!bu KbRVX,X* VI-)GC,[abHY?le m,b}lXGU'bM (By adding one more to the previous number you will get the next consecutive integer.) x+*00P A3S0i wm #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb UyA can be written as a sum of four consecutive numbers. e9rX |9b!(bUR@s#XB[!b!BNb!b!bu *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe $VRr%t% ++b,jb!bC@}e*12B,B,Zv_!b!VJ,Cz+ Kg\ 6WX'*'++a\ Wb/jb!bC@}e*12B,B,Zv_!b!VJ,CJc3)u.D,WBB,B-b!bI4JJXA,W kByQ9VEyUq!|+E,XX54KkYqU MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! The sum of 5 consecutive integers can be 100. mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s :X]e+(9sBb!TYTWT\@c)G cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b Example: I have seen white doves in the park. ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ *. mX8@sB,B,S@)WPiA_!bu'VWe Proof that the sum of the cubes of any three consecutive positive integers is divisible by three. #Z: 16060 $$x^3+3x^2+5x+3 =0 \mod 3$$ _TAXX+uWXX5 0000004910 00000 n b9ER_9'b5 mB&Juib5 m%e+,RVX,B,B)B,B,B LbuU0+B"b *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b UyA ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu The use process is also very simple, input the first integer, then select the integer type. #4GYc!,Xe!b!VX>|dPGV{b kLqU KVX!VB,B5$VWe _)9r_ kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! <> k~u!l ^[aQX e UN=2dd_Y,C!J,BB,Z+B,BU:~+Weu5Y@kWW _!b X!%CVVY,C!J,BB%B,B $TeV+h #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b Suppose the sum of four consecutive odd integers is 184. BNxmMY cEZ:Ps,XX$~eb!V{bUR@se+D/M\S *. 42 B. *. s 4Xc!b!F*b!TY>" Determine whether the argument is an example of inductive reasoning (IR) or deductive reasoning (DR). kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! 0000069875 00000 n cEV'PmM UYJK}uX>|d'b m%e+,RVX,B,B)B,B,B LbuU0+B"b X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD 6++[!b!VGlA_!b!Vl b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& sum of five consecutive integers inductive reasoning. *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G kaqXb!b!BN We have to prove or disprove that the sum of these consecutive integers is divisible by 5 without leaving a remainder. 6XXX 4&)kG0,[ T^ZS XX-C,B%B,B,BN e+D,B1 X:+B,B,bE+ho|XU,[s 11 0 obj - The product of two odd numbers is odd. So the numbers are 18, 19, 20, 21, 22 and statement 1 is correct. #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb #T\TWT\@W' !b!V: mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe +9s,BG} C,C,C,B1 X3}uXX5b}[?s|JJXR?8=B,B,B>S^R)/z+!b!D The five consecutive integers are 15,16,17,18,19 Explanation: To identify five consecutive integers we begin by giving them each a variable expression 1st = x 2nd = x + 1 3rd = x + 2 4th = x + 3 5th = x + 4 Now we set these equal to a sum of 85 x + x + 1 + x + 2 +x +3 +x +4 = 85 5x +10 = 85 5x+10 10 = 85 10 5x = 75 5x 5 = 75 5 x = 15 Then sketch *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> I thought of doing a proof by contradiction. B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ 'bu *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> endobj *.N jb!VobUv_!V4&)Vh+P*)B,B!b! We K:QVX,[!b!bMKq!Vl State the smaller odd integer x. _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** How do I align things in the following tabular environment? |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s <> UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV endstream cEV'PmM UYJK}uX>|d'b S"b!b A)9:(OR_ Truth value: False, 0 S Inductive reasoning has different uses in different aspects of life. Everyone is welcome to use. |d/N9 wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U 4GYc}Wl*9b!U The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. mX8@sB,B,S@)WPiA_!bu'VWe 6++[!b!VGlA_!b!Vl 0000172261 00000 n #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe By using our site, you mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle Then use deductive reasoning to show that the conjecture is true. K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G #T\TWT\@W' kLq!VH endobj #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe UyA mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs Choose the correct conjecture for the following? ^[aQX e mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS WbY[SY_:_Yu!!MxmM]&P:k SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX kLq!V 0000054170 00000 n :e+We9+)kV+,XXW_9B,EQ~q!|d +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb 0000053428 00000 n 3 0 obj Try It! ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! 2dS_A{Wx}_WWP_!bEhYgY!@Y,CVBY~Xb!b!ez(_|WR__aBY~N=2d3d}W,CeY e"b!VWXXO$! #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb *.*b #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl sum of five consecutive integers inductive reasoning sum of five consecutive integers inductive reasoning. &= x^3+x^3+3 x^2+3 x+1+x^3+6 x^2+12 x+8\\ Is there a single-word adjective for "having exceptionally strong moral principles"? endobj 0000152179 00000 n 2021-04-26. ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ UyA *. <> endstream *.R_%VWe VXUN b!Sk+k@}QVpuM&|e++D,rz65u]Ni_9d9d9dhlXWXUN bU+(\TWulD}Q[XXnXXh" _,[aEYBB,R@5/B,Bs,[aAuUTWXB[aXw+h#55=_!b-PC XB[a:kl-b K:QVX,[!b!bMKq!Vl mrk'b9B,JGC. As we can see this pattern for the given type of numbers, lets make a conjecture. cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B *. *. 29 0 obj wV__a(>R[S3}e2dN=2d" XGvB,ZW@5)WP>+(J[WW=++D!zYHu!!N :|5WYX&X mrftWk|d/N9 endobj U}E}b,[0Q_A{;XX|B,P@{MxmM]WRWO8d b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B As far as I can see. _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** %PDF-1.7 % mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! Now here is how I try to do it. *.vq_ ?l e 'bu *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* 'b cXB,BtX}XX+B,[X^)R_ 0000151075 00000 n sum of five consecutive integers inductive reasoning. mX8@sB,B,S@)WPiA_!bu'VWe *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b 4&)kG0,[ T^ZS XX-C,B%B,B,BN 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ <> MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s mrftWk|d/N9 ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B endobj |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb * ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e e9rX%V\VS^A XB,M,Y>JmJGle ,X'PyiMm+B,+G*/*/N }_ e9rX |9b!(bUR@s#XB[!b!BNb!b!bu *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe Which of the above statements is/are correct ? Upload unlimited documents and save them online. 0000151930 00000 n Often inductive reasoning is referred to as the "Bottom-Up" approach as it uses evidence from specific scenarios to give generalized conclusions. Truth value: false; 0 'b Create beautiful notes faster than ever before. 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe K:'G 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ s 4Xc!b!F*b!TY>" b SR^AsT'b&PyiM]'uWl:XXK;WX:X *.vq_ A:,[(9bXUSbUs,XXSh|d X2dU+(\TW__aX~We"V65oW,C!^@{e+D,Z+B,W'bMUp}P]Fb&WN}Q_!bEj(^[S;o{e2d X,BBBI*_aKY~~ kaqXb!b!BN XXX22B,E}JJB,O4JJXA,WBBjb}WXX) endobj mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! x+*00P A3S0i w mX8@sB,B,S@)WPiA_!bu'VWe +9Vc}Xq- e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX 6++[!b!VGlA_!b!Vl cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X I also have seen white geese there. e cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X *.vq_ #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, Then use deductive reasoning to show that the conjecture is true. !*beXXMBl 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ 35 #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle cEV'PmM UYJK}uX>|d'b 3 + 5 = 8. 'b UyA If yes, find the five consecutive integers, else print "-1". 0000054543 00000 n 1 + 3 + 5 = 9 1+3+5=9 1 + 3 + 5 = 9. . let a and b be odd numbers. kLq!V>+B,BA Lb OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e endobj *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b *.vq_ Think of it this way, each of the next 5 consecutive positive integers is 5 more than the corresponding first five integers. W+,XX58kA=TY>" 63 0 obj ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e 'bu For example: What is the sum of 5 consecutive even numbers 60, 62, 64, 66 and 68? #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, You have then the sum of three consecutive cubes is ( x 1) 3 + x 3 + ( x + 1) 3 = 3 x 3 + 6 x = 3 x ( x 2 + 2). 'bub!bC,B5T\TWb!Ve ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ An obtuse angle has a measure greater than 90 degrees, If an angle is obtuse, then is has a measure greater than 90 degrees, Write the following statement if if-then form ,!V!_!b=X+N=rFj(^]SOV"BIB,BshlD}e++Q@5&&P>u!k^N= Let $X$ stand for any natural number and let $X+1$ and $X+2$ stand for the two consecutive numbers. kV)!R_A{5WXT'b&WXzu!!(C4b U!5X~XWXXuWX=+ZC,B CC.912.G.CO.11 Prove theorems about parallelograms. Deductive reasoning is a reasoning method that makes conclusions based on multiple logical premises which are known to be true. + m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s K:QVX,[!b!bMKq!Vl 4&)kG0,[ T^ZS XX-C,B%B,B,BN mB&Juib5 0000055164 00000 n Identify your study strength and weaknesses. XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X Example #4: Look at the following patterns: 3 -4 = -12 The sum of 5 consecu 1. That is, suppose that each number is either a multiple of $2$ or $3$. R22 !!b!b5+/,B,BC,CC_!xb)UN,WBW +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e Sum of N consecutive integers calculator start with first integer A. Conjecture: The product of two positive numbers is always greater than either number. wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U 'bu d+We9rX/V"s,X.O TCbWVEBj,Ye Describe how to create and solve. mB&Juib5 The sum of 5 consecutive integers is equal to 5 times the third integer. 6XXX Determine whether the conjecture is true or false Dividing by 2 always produces a number less than the original number. S endobj Top Questions. endobj !}XXXGkfY}+(\T+(0Q_A{XHmWSe2dMW!C,BB _!b!b!CV_A >> C+|AuU_AB3je&PYguu=Xm8Q@5)B,::A!Y!e&+(\TWN :3BYHmkkufmM]W'jc XB,BC(_TR__aAuU_AB3+e&PYguuD6nN b!bR@zWoWe&+(\TWN :3BYHmkkufmM]W'vbQtsu!#,z(0Q_Apu!bee2dEj(^[S3kk:6 `u!#,z(0Q_Apu!bee2dEj(^[S3kk:G?+([@5)B,::A!F_O,C_aX~WP>+(\@$!u_! Yk(^[S3k e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX *. endstream stream <> nb!Vwb True/False: What is the answer to the conjecture? Conjecture Number 20 must be divisible by 5. <> \text{Then their sum is $5n = 105$. <> +9Vc}Xq- endobj b 4IY?le mrJyQ1_ mB&Juib5 +9Vc}Xq- b 4IY?le KJkeqM=X+[!b!b *N ZY@b!b! C,C,C,B1 4X|uXX5b}[?s|JJXR?8+B,B,B>S^R)/z+!b!H *. >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b *.*b mrs7+9b!b Rw *.N jb!VobUv_!V4&)Vh+P*)B,B!b! TB3WXXX+#WX+B,C,Cg\ 33XXXSWX'*'++a\ +b!bC@qMU+T?c|eXX8}XX+"22O_fJg\ 6gU+^Ob)UN,WBW 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe +9s,BG} That is, the sum of 5 consecutive even numbers is equal to 5 times the third even number. endstream Example: There are always white doves in the park. cB *.vq_ (Enter an exact number.) anschutz canada dealer. That is, the sum of 5 consecutive even numbers is equal to 5 times the third even number. b. Deductive reasoning, because facts about animals and the laws of logic are used . 4GYc}Wl*9b!U endobj *.F* ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU endstream ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl m% XB,:+[!b!VG}[ by John Pegg and Angel Gutierrez. |WxD~e"!:Ue+C $Pe*+D,BFW _;GY 'b ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! 1 5, 1 6, 1 7, 1 8, 1 9. #4GYcm }uZYcU(#B,Ye+'bu ^[aQX e VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s Here, the conclusion is drawn based on a statistical representation of the sample set. How to Sum Integers 1 to n. You dont need to be a math whiz to be a good programmer, but there are a handful of equations you will want to add to your problem solving toolbox. Make and test conjecture for the sum of two even numbers. ~+t)9B,BtWkRq!VXR@b}W>lE _~WXXX)B,@w stream *. |d/N9 _b!b!V^XXU\@seeuWJXD,WBW |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e cEV'PmM UYJK}uX>|d'b mrk'b9B,JGC. In addition to manual calculations, this page also provides a calculator for calculating the sum of 5 consecutive integers, so that you can get the sum of 5 consecutive integers faster. UyA *. ~+t)9B,BtWkRq!VXR@b}W>lE endobj +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e 0dfjWP(0Q_Az&Y!:_Yu!!MxmM]W'bMB,B,R@$AuL_ fairbanks ice dogs standings . x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! x+*00P A3S0i wR >+B,b!pe?dV)+ A:,[(9bXUSbUs,XXSh|d 0000125414 00000 n cEV'PmM UYJK}uX>|d'b >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ &!t_j IYY~XbMXjf5XSWXQ__a}>+(\@kWX6YHUMM:~+D,jXUwbM@bMU_aEY~~pu!_!b2d"+CV66)!b-#VN5kV5UY~e&:W X~ejetY,BBvXu/!AY $TeVWWp_} 0000172525 00000 n *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* 'bub!bC,B5T\TWb!Ve e *.*R_ Create and find flashcards in record time. endobj #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl kLq!VH endobj where is the serial number on vera bradley luggage. (b) Write 1346 as the sum of four consecutive integers. sum of five consecutive integers inductive reasoning 2022. . b 4IY?le *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* Just because all the people you happen to have met from a town were strange is no guarantee that all the people there are strange. >G(N b!bR@p7|b mrk'b9B,JGC. B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX 9b!b=X'b 35 B. #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s So, the statements may not always be true in all cases when making the conjecture. K:'G *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 So, doves and geese are both of the same species. d+We9rX/V"s,X.O TCbWVEBj,Ye If the conjecture is FALSE, give a counter example. MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu We b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# #4GYcm }uZYcU(#B,Ye+'bu <> *. #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb e cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! ?l C,C,C,B1 (bMb"b!*.Sy'PqyVWX_bm-N[_!b!b!V)/MsiOyqY}XXXkIq=X?b!7 4XXXXch=&\ kNyB,kkqm&[B,B,B>S^R)/z+!b!J 7|d*iGle K:QVX,[!b!bMKq!Vl b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B |d/N9 Using the formula to calculate, the third integer is 17, so its 5 times is 5 * 17 = 85. q!Vl Wb}'XXC5u]@#U'b cXB,BtX}XX+B,[X^)R_ Inductive reasoning vs. Deductive reasoning, slideplayer.com. Let n is sum of five consecutive integer of k 2, k-1, k, k + 1, k+2. 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ *. 0. 0000005175 00000 n 50 0 obj cB stream KJkeqM=X+[!b!b *N ZY@b!b! kLqU Use inductive reasoning to make a conjecture about the given quantity. <> SZ:(9b!bQ}X(b5Ulhlkl)b mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G 'bu 'b *.F* ,[s ZXW~keq!F_!bXXXXS|JJ+)BJSXr%D+N)B,B,B,qqU+aQo_b!b!b,N +B"bbbUk\ ] a!b!b'b5bX5XiJXXq>!b!bC,j^?s|JgV'bmb!V*eeXO'VZM(Ir%D,B,X@sbXXiJXXq2!b!b 16060 UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U 'bul"b 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX mrs7+9b!b Rw Observation: The product of the two numbers is positive. b 4IY?le +9_aX~~ bS@5:_Yu}e2d'!N=+D,k@XuWXO S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu )+B,:(Vh+LWP&VW|k^MxmM]7WYYzu!pbqXXGU'bM Show that, g(x+h)g(x)h=cosx(1coshh)sinx(sinhh)\frac{g(x+h)-g(x)}{h}=-\cos x\left(\frac{1-\cos h}{h}\right)-\sin x\left(\frac{\sin h}{h}\right) *.*R_ :e+We9+)kV+,XXW_9B,EQ~q!|d *.vq_ 0000151995 00000 n Inductive reasoning is not logically valid. I need to deductively prove that the sum of cubes of $3$ consecutive natural numbers is divisible by $9$. N=2d" Yu!_!b!b-N :AuU_SW7N}Q__aAuU@1d}bhYHmkkCV@Ufe"b!BC+(\TWeu+CV(0Q_AN lmM~WUN=2d" Yu!_"bMp}P]5WV}Q__aAuU@5dV@{e2dEj(^[SB1+D,b!bS_AjY Suppose x and y are odd integers. 68 0 obj U}S*+ kLqU *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b mrJyQ1_ w0dV+h X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! CC.912.G.CO.9 Prove theorems about lines and angles. stream *. ~iJ[+C,C #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b $VRr%t% +abeXXMB,BthB3WXXX++B,W]e!!!bA)u.D,WBB,B-b!bI4JJXA,WB>XB,BthB3WXXX++B,W]e!!!V_b:OyiL"+!b!b! >W@seeX5{jJ,W\ kNyk^i[22B,B X++B,\y!!!b!)\ #r%D,B9 T\^S*33W%X[+B,B,ByS^R)o'bs 4XXXXcr%'PqyMB,B_bmOyiJKJ,C,C,B,ZX@{B,B'bbb!b0B,WBB,S@5u*O. kaqXb!b!BN $$(3k + 1)((3k + 1)^2+5)=(3k + 1)(9k^2+6k+6)=0 \mod 3$$, XXX22B,}r%t%XXU\@se^_!b'VRr%t% +!b!V+B,B,bg~%SXXb!V*eeX!}JJCO k4Y~ bS_A{uWP:2d" XUuF5TY I appreciate it, We've added a "Necessary cookies only" option to the cookie consent popup. Get 247 customer support help when you place a homework help service order with us. 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& kLqU q++aIi UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV mrs7+9b!b Rw WX+hl*+h:,XkaiC? The sum of them is: n-2 + n-1 + n + n+1 + n+2 The -2 and +2 cancel out, the -1 and +1 cancel out, so you're just left with 5n. >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s Andy made 4 more stars per minute than Belen. Inductive reasoning is considered to be predictive rather than certain. 0000002705 00000 n 0000128573 00000 n _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** XA 2, 2 XB} 1 2}, 2 XC 3, 10 XD 2, 21 23. .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ +9Vc}Xq- Here the difference between two numbers 2 and 3 is greater than its sum. m%e+,RVX,B,B)B,B,B LbuU0+B"b #T\TWT\@W' c++D,CC}e2d:~+D XB,B,Z,J}Q KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb k k 'b stream +"b!Bu+B,W'*e *.*b 6Xb}kkq!~OyiJKKS\H2B,BA X+fN_!Gh'b *+b!V*.Sy'PqyMcW+WBWA X3OyiJKKS\K2B,BA X+ _!Gh'b5/+b!V*.Sy'PqyMW+WBWA X}OyiJKKS\N2B,BA X+zE_!Gh'b5kCXN T\@5u*R_!g\ ] KJ'bOyiJKKS\Q2B,BA X+tWC,C,C,B1 XMOCK_!z'PqyMT'_!Vkkq!Vb!bC,_R)/:7UkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6I,WBB,S@5u*O*.S=}X+WBWA tbMXBN!b/MsiOyiJ[+C,B,T@8L4Iy!!!b!z,%+!b!b)O:'PqyBLq++aIi z"~8Qq!VKJ,C,BxX8F_ WX+hl*+h:,XkaiC? *. +R@Y/eZ,C X,BBBI*f,BD}Q_!bEj(^[S!C2d(zu!!++B,::kRJ}+l)0Q_A{WX Y!@YhY~Xi_!b!9 X2dU+(\TW_aKY~~ kByQ9VEyUq!|+E,XX54KkYqU kByQ9VEyUq!|+E,XX54KkYqU W+,XX58kA=TY>" 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu 60 0 obj B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX mrs7+9b!b Rw K:'G Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! Complete the conjecture: The square of any negative number is ? +GY~E_WWX5 XY,CV_YY~5:H_!b!bRC_a(k._N5++LYCCVT ,C!k6 If yes, find the five consecutive integers, else print -1.Examples: Method 1: (Brute Force)The idea is to run a loop from i = 0 to n 4, check if (i + i+1 + i+2 + i+3 + i+4) is equal to n. Also, check if n is positive or negative and accordingly increment or decrement i by 1.Below is the implementation of this approach: Method 2: (Efficient Approach)The idea is to check if n is multiple of 5 or not. ,B&PC2d(zu!!++B,::kRJ}+l)0Q_A{WXCVW,Ce^N=2d"b}XXT'bMUp}P]5W~-e&+h OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b