e+D,B,ZX@qb+B,B1 LbuU0R^Ab endobj Pattern: Conjecture: _____ Test: DISPROVING CONJECTURES Example 5 Show that the conjecture is false by finding a counterexample. A:,[(9bXUSbUs,XXSh|d *.R_ 0000144950 00000 n XA 2, 2 XB} 1 2}, 2 XC 3, 10 XD 2, 21 23. XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X *.R_ *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! What sort of strategies would a medieval military use against a fantasy giant? Stop procrastinating with our smart planner features. 0000136995 00000 n UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! Endpoints of a diameter: (0, 0, 4), (4, 6, 0), Let g(x)=cosxg(x)=\cos xg(x)=cosx. 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: UyA 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b Sum of Five Consecutive Integers Calculator. 0000003418 00000 n b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! s 4XB,,Y x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! kLqU For example: What is the sum of 5 consecutive integers 15, 16, 17, 18 and 19? =++DceZ+C!k~u!!MxuM!nb!BI!VAuU_AE,w+h 6XjH7|Xq++aIi B]byiK4XOb!bV'b@kLq! log(x+2)log(x1)=log(x+2)log(x1)\frac { \log ( x + 2 ) } { \log ( x - 1 ) } = \log ( x + 2 ) - \log ( x - 1 ) can be written as a sum of four consecutive numbers. endobj mX+#B8+ j,[eiXb bbb!TbWjXXU\@suW"M4JJXA,WBCkEXXXo_}Xok~XXXXb+ZbEeeUA,C,C,DpA }X=h [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e To make a conjecture, we first find a pattern. #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ cB cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X Inductive Reasoning Inductive Reasoning Inductive Reasoning Calculus Absolute Maxima and Minima Absolute and Conditional Convergence Accumulation Function Accumulation Problems Algebraic Functions Alternating Series Antiderivatives Application of Derivatives Approximating Areas Arc Length of a Curve Area Between Two Curves Arithmetic Series 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b For example, if you leave for work and it's raining outside, you reasonably assume that it will rain the whole way and decide to carry an umbrella. A:,[(9bXUSbUs,XXSh|d b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! We endobj nb!Vwb stream bWb!b!b!b!bWO V^S*.12B,B,}JXX+"22'+Msi$b"b!b5B,B,z&*'++ay%0B,B,B,B,z@N T\?c|eXX/j5UWbbEeeuWO VR)/Ir%D,B,j}XXLb)UN,WBW 0000172525 00000 n 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 +9s,BG} *. <> 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b +9Vc}Xq- k^q=X B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb * mrk'b9B,JGC. !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu 72 0 obj e9rX%V\VS^A XB,M,Y>JmJGle So, the next dove which comes will also be white. *.*R_ N b!bR@uF+B,VN}(Vf}QXX)3kkC!C,,[a:B}WXXp}P]RWX1e Does either approach prove that the sum of five consecutive integers; Question: Reasoning 1. l = last term. OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e *.R_ #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl 0000151075 00000 n #T\TWT\@W' W'b"!M,C!+2djh endobj #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ mX+#B8+ j,[eiXb a) Describe two different algorithms for finding a spanning tree in a simple graph. 4GYc}Wl*9b!U 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. Top Questions. sum of five consecutive integers inductive reasoning I also have seen white geese there. #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 ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We Describe how to sketch the fourth figure in the pattern. We [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 KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! This reasoning is also used in scientific research by proving or contradicting a hypothesis. mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs qWX5 B:~+TW~-b&WN}!|e5!5X,CV:A}XXBJ}QC_a>+l0A,BeTUW,CxbYBI!Cb!b *GY~~_aX~~ b"VX,CV}e2d'!N b=X_+B,bU+h *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* ,[0Q_AN &_ 'bub!bC,B5T\TWb!Ve q!Vl 47 0 obj endobj \text{Then their sum is $5n = 105$. #4GYcm }uZYcU(#B,Ye+'bu s 4XB,,Y cEV'PmM UYJK}uX>|d'b True statement My dog is brown. 'bu _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L ,BB:X+C!k~u!!MxuM!b!BI!VAuU_AdE,w+h ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ :e+We9+)kV+,XXW_9B,EQ~q!|d mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs i_a:kYu!V@e+L(++B,7XS5s*,BD}&E}WN5+D,C!kxu)}e&&e ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* kaqXb!b!BN 0000002705 00000 n ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ |d/N9 What is an all, always, every venn diagram? cB ,B,HmM9d} b9duhlHu!"BI!b!1+B,X}QVp}P]U' bVeXXOTV@z!>_UCCC,[!b!bV_!b!b!bN|}P]WP}X(VX=N :}5X*rr&Pk(}^@5)B,:[}XXXSe+|AuU_AnPb,[0Q_A{;b!1z!|XC,,[a65pb}*VXQb!b!B#WXXie b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle m%e+,RVX,B,B)B,B,B LbuU0+B"b This. ,Bn)*9b!b)N9 e9rX%V\VS^A XB,M,Y>JmJGle So $n = 21$.} #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX Inductive reasoning is considered to be predictive rather than certain. KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb *.N jb!VobUv_!V4&)Vh+P*)B,B!b! #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, Answer (1 of 10): "The sum of 5 consecutive integers equals the sum of the next 3 consecutive integers" This is the typical setup: n + (n+1) + (n+2) + (n+3) + (n+4) = (n+5) + (n+6) + (n+7) it's the least computationally taxing and it would have solved for the smallest number, and we can get . *. *.R_%VWe [+|(>R[S3}e2dN=2d" XGvW'bM #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe *. KbRVX,X* VI-)GC,[abHY?le MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie *.R_%VWe wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U *.F* +JXXXXWh1zk\ WXXX+9r%%keq!VM *.R_%VWe *.F* How to prove that the difference between an even integer and an odd Integers are three types of numbers including negative integers, positive integers and zero. endobj moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l Write the inverse, converse, and contrapositive of the conditional statements below. mX8@sB,B,S@)WPiA_!bu'VWe 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. DXX 6JzYs-m65292023591 - > > ()4~7 . Given that $a$, $b$, $c$ are natural numbers, with $a^2+b^2=c^2$ and $ c-b=1$, prove the following. WX+hl*+h:,XkaiC? 36 0 obj 'bu [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b 42 0 obj CC.912.G.CO.9 Prove theorems about lines and angles. >> 'Db}WXX8kiyWX"Qe An example or case which proves conjecture is called a counterexample. #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X X2dU+(\TWu__aX~We"V65u;}e2d X,BB+B,W'bMUp}P]RW~~!bS_A{WX9C[2dYC,C_!b!_!b!V:kRJ}++ #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl m b 6XXX ?l B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX PDF Homework 8 - Mathematical Sciences B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX 'b We b 4IY?le moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B e You have then the sum of three consecutive cubes is $(x-1)^3+x^3+(x+1)^3 = 3x^3+6x=3x(x^2+2)$. Conversely, deductive reasoning is more certain and can be used to draw conclusions about specific circumstances using generalized information or patterns. |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb m% XB,:+[!b!VG}[ In inductive reasoning, true observations might have false conjecture. _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L q++aIi @*b!VBN!b/MsiR"2B,BA X+WXhg_"b!*.SyR_bm-R_!b/N b!:Oyq,U++C,B,T@}XkLq2++!b!b,O:'Pqy5 !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe |d/N9 These start with one specific observation, add a general pattern, and end with a conclusion. k UyA <> e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- For example: What is the sum of 5 consecutive even numbers 60, 62, 64, 66 and 68? be_@{e2dEj(^]SuW'bM :X]e+(9sBb!TYTWT\@c)G Example #4: Look at the following patterns: 3 -4 = -12 To To prove that a conjecture is true, you need to prove it is true in all cases. G NX~XXV'P>+(\CQ_Z+|(0Q@$!kY+2dN=2d" ) _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L It's true when $x=0 \mod 3$. Try It! The sum of two consecutive integers is 5, what are the integers? ,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 :X]e+(9sBb!TYTWT\@c)G Sum of Integers Formula: S = n (a + l)/2. <> |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s Conjecture: The product of two positive numbers is always greater than either number. Choose the correct conjecture for the following? 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: = 2n . !b!V: Then use deductive reasoning to show that the conjecture is true. x+*00P AC(#9KP%+ Multiple Choice Which of the following is a counterexample of the conjecture below? &4XS5s*,BDW@kWX5TY,CN!V@uWXQb!b=X_+B,@bMU! In this tutorial, you learned how to sum a series of consecutive integers with a simple and easy to remember equation. #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, 0000155651 00000 n junio 16, 2022 . Get the Gauthmath App. X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d e+D,B1 X:+B,B,bE+ho|XU,[s MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV mrJyQ1_ #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 stream _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe endobj Example: 7 doves out of 10 in the U.S. are white. kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! C,C,C,B1 (bMb"b!*.Sy'PqyVWX_bm-N[_!b!b!V)/MsiOyqY}XXXkIq=X?b!7 4XXXXch=&\ kNyB,kkqm&[B,B,B>S^R)/z+!b!J 12 0 obj endobj mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s 4GYc}Wl*9b!U Sorry for the late reply. b 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe mX+#B8+ j,[eiXb U})E}e+e+|>kLMxmMszWUN= Here we will understand what inductive reasoning is, compare it to related concepts, and discuss how we can give conclusions based on it. *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD a. VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s k~u!B,[v_!bm= )#j(^[S MxmM]W'FN b!bR@zg_ 'Db}WXX8kiyWX"Qe K:QVX,[!b!bMKq!Vl cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ d+We9rX/V"s,X.O TCbWVEBj,Ye ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X mrs7+9b!b Rw Here, the product of both the numbers is 10, which is positive. 'b k~u!AuU_Ajj,*VX=N :>6'b9d9dEj(^[S n+Vzu!|J WUDYBB,R@uduB,,[0Q_Apu=XmPe+|>kLMxmM9dY[SCV:Vh+D,ZS@$yR5:kRXO!p}PWX(Vh+LWP+w,Bzuumk(^UJ,Nu!T'C[B,B,BI ,[s 2 The product of three consecutive natural numbers can be equal to their sum. ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl The sum of three consecutive integers is #Z: 5(n +2) If we divide this sum of any 5 consecutive integers by 5 we get: 5(n + 2) 5 . stream WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d 0000073873 00000 n 4GYc}Wl*9b!U Make a test a conjecture about the sum of any three consecutive integers. 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 *.*R_ e ,Bn)*9b!b)N9 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 mrJy!VA:9s,BGkC,[gFQ_eU,[BYXXi!b!b!b!b')+m!B'Vh+ sW+hc}Xi s,XX8GJ+#+,[BYBB8,[!b!b!BN#??XB,j,[(9]_})N1: s,Bty!B,W,[aDY X: stream ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b SInce there are 5 integers, 5x5 would make the sum 25 greater than A. <> #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl kLq!VH 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: 0000072332 00000 n cEZ:Ps,XX$~eb!V{bUR@se+D/M\S cXB,BtX}XX+B,[X^)R_ 4GYc}Wl*9b!U 65 0 obj How do I find the angles of an isosceles triangle whose two base angles are equal and whose third angle is 10 less than three times a base angle? #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb e+D,B1 X:+B,B,bE+ho|XU,[s 27 0 obj 6XXX 'bul"b As far as I can see. WbY[SY_:_Yu!!MxmM]&P:k 6'bbb!b0+WBWBB,ZY@5ukOq++aIi V+_!b!BN!b/Ms}eeU+C,B,T@WXW_"b!*.S=}XX{g\ ] KJZ stream ?l Test your knowledge with gamified quizzes. mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe The sum of five consecutive integers, as the name implies, requires the addition of five consecutive integers. *Vs,XX$~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 X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d cEV'PmM UYJK}uX>|d'b cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X mrk'b9B,JGC. ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! In addition to calculating the sum of 5 consecutive integers, you may also need to calculate the sum of 5 consecutive even numbers, or the sum of 5 consecutive odd numbers. mX+#B8+ j,[eiXb 33 0 obj ~+t)9B,BtWkRq!VXR@b}W>lE _)9r_ 17 0 obj #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl 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 6++[!b!VGlA_!b!Vl 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: Learn more about Stack Overflow the company, and our products. 4GYc}Wl*9b!U SR^AsT'b&PyiM]'uWl:XXK;WX:X ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B <> 'bul"b endstream wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U endobj 42 B. k>" W'bV@5)B,::kR_Ap}+h|B,HmM9dY[SbKU'b9d For building our understanding of the world, inductive reasoning is used in day-to-day life. _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b N bU+(\TWbe+&+h|N|B,::!!+R@nZ mX8@sB,B,S@)WPiA_!bu'VWe mB&Juib5 +DYHeO,C!+R@5):X_!b!R_A{WWp_WW _!bee2dE:W,CxbYBI! "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ ,X'PyiMm+B,+G*/*/N }_ #Z: <> acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Data Structure & Algorithm-Self Paced(C++/JAVA), Android App Development with Kotlin(Live), Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Number expressed as sum of five consecutive integers, Represent the fraction of two numbers in the string format, Check if a given array contains duplicate elements within k distance from each other, Find duplicates in a given array when elements are not limited to a range, Find duplicates in O(n) time and O(1) extra space | Set 1, Find the two repeating elements in a given array, Duplicates in an array in O(n) and by using O(1) extra space | Set-2, Duplicates in an array in O(n) time and by using O(1) extra space | Set-3, Count frequencies of all elements in array in O(1) extra space and O(n) time, Find the frequency of a number in an array, Count number of occurrences (or frequency) in a sorted array, Merge two sorted arrays with O(1) extra space, Efficiently merging two sorted arrays with O(1) extra space, Program for Nth node from the end of a Linked List, Write a function that counts the number of times a given int occurs in a Linked List, Add two numbers represented by Linked List, Add two numbers represented by linked lists | Set 2, Add two numbers represented by Linked List without any extra space, Tree Traversals (Inorder, Preorder and Postorder). b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B +C,,Hmkk6 XloU'bM 16 0 obj +DHu!!kU!@Y,CVBY~Xg+B,XGY~#~mYO,B '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 nb!Vwb .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ e 'b q!VkMy +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG *f ?l endobj of the users don't pass the Inductive Reasoning quiz! 0000094672 00000 n !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe b 4IY?le X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 41 0 obj The general unproven conclusion we reach using inductive reasoning is called a conjecture or hypothesis. 2. bbb!b!)z~a!b!b'bbb|X}uXr%D,B9]b!b!bu)9r%t%,iAXXi_=XXX22B,BUSbB,B,*.O922 UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV U}WCu kLqU kSu!R_Anb!VHYB[a(w,. e XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** 0000053987 00000 n mrftWk|d/N9 'bul"b *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD let a and b be odd numbers. stream *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* 0000068151 00000 n b9ER_9'b5 7|d*iGle e Show all of your work. endobj 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie Now here is how I try to do it. m%e+,RVX,B,B)B,B,B LbuU0+B"b endobj s 4Xc!b!F*b!TY>" x -qo@"EyCv?Oc?/?='rvx`??j; b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B 0000005784 00000 n stream 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! b9ER_9'b5 WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle s 4XB,,Y >> kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* sum of five consecutive integers inductive reasoning So, the given conjecture is false. cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ +DHu!!k!@Y,CVBY~Xb!b!ez(p0+ c++D,CC}e2d:~+D XB,B,Z,J}Q 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ In math, what does reciprocal mean? endstream K:QVX,[!b!bMKq!Vl x+*00P A3S0i wv *.vq_ s 4Xc!b!F*b!TY>" X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 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 2d++Lu_+(\@5(C!k6YYTmmR_!b!b!b!be+L0A Sum of Five Consecutive Integers Video. XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X mX+#B8+ j,[eiXb W+,XX58kA=TY>" endobj mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab *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 m #4GYcm }uZYcU(#B,Ye+'bu +D:_Yu!!+K6Y+e2dM+v%B9!nbMU!p}Q_aDYm)WW _!b'hY)2dYYmMXXb!k7*kWP(6eu4X~~ b"xb:u4,C!uT\YX5Xm!b!b(p}Q_\b&WXuC,CteYcB,B9jC!b=XS5s+(\_A{W JSXw%XXXXX/6j5UWbbEe!V@4S^?JXXWXX$VRr%t% +k|!b!b!b!b!}b5u*O+C,B,B%D,Bx }XXbb=eJ_=XiJK&kI4JJXAWC,B,B,B,z4z:'Pqq!b!b!F_"b!VJ,C6Rz:OyiL"+!b!b!>_!b!b=XiJXY_=`XXXX#VW?k_ +^C_u%!VXXXi[OyiJK&k~@,B,z$*'++a_ X+KXXB~ T\^S*.12B,B,WBB,W]e!!!VSOyiJK&_h q!Vl #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b 'bub!bC,B5T\TWb!Ve [+|(>R[S3}e2dN=2d" XGvW'bM 9b!b=X'b 'bu So about 70% of doves in the U.S. are white. mrftWk|d/N9 endobj e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e q!Vl +9s,BG} _)9r_ k b"b! sum of five consecutive integers inductive reasoning sum of five consecutive integers inductive reasoning. Deductive reasoning is a reasoning method that makes conclusions based on multiple logical premises which are known to be true. q!VkMy endobj Here the difference between two numbers 2 and 3 is greater than its sum. *. mB&Juib5 q!Vl Do you agree that after your correction all we have to prove is $x^3+5x$ is always a multiple of $3$? 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 *.*R_ |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s |d/N9 cB _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L WX+hl*+h:,XkaiC? k4Y~ bS_Aeu}WxD~e"!:Xm\i *UQ_!b!b}%BB,CVEY~~ Conjecture: The sum of the first n odd positive integers is __?__. cB 4GYc}Wl*9b!U 4GYc}Wl*9b!U stream #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe kaqXb!b!BN x+*00P A3S0i wR <> kV)!R_A{5WXT'b&WXzu!!(C4b U!5X~XWXXuWX=+ZC,B Determine whether each equation is true or false. Try It! !MU'b It may be more useful to have the center number be $x$, and the two numbers to either side be $x-1$ and $x+1$. ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B 'b mB&Juib5 0000056695 00000 n *.N jb!VobUv_!V4&)Vh+P*)B,B!b! GV^Y?le _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** If the sum of five consecutive positive integers is A, then the sum of ,[s Upload unlimited documents and save them online. m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L kLq!VH 'b 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! 0000084754 00000 n ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B ,Bn)*9b!b)N9 +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e k^q=X From the above, we can observe that the answer of all the sums is always an even number. #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb nb!Vwb *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 CONTACT; Email: Inventory Management Strategies Of Canadian Tire, How To Create 15 Minute Time Intervals In Excel, New Balance Indoor Nationals 2022 Standards. !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe YhYHmk 9b!b=X'b XXX|uXXX22B,Bb!b!C,C,CU[b)UN,WBW mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s A hypothesis is formed by observing the given sample and finding the pattern between observations. b"b!. XXX|uXXX22B,Bb!b!C,C,C%z+MrbVWX Select the smallest value of P that satisfies given conditions. *.R_ mrJy!VA:9s,BGkC,[gFQ_eU,[BYXXi!b!b!b!b')+m!B'Vh+ sW+hc}Xi s,XX8GJ+#+,[BYBB8,[!b!b!BN#??XB,j,[(9]_})N1: s,Bty!B,W,[aDY X: 6++[!b!VGlA_!b!Vl +MrbV}XXX+WWV'buq+E,C,C 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: 3. vegan) just to try it, does this inconvenience the caterers and staff? mX8@sB,B,S@)WPiA_!bu'VWe *. stream _)9r_ mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! cEZ:Ps,XX$~eb!V{bUR@se+D/M\S 0000005175 00000 n Xg&P|b: X,CV65u]@5zW~XXgV'P>9dF_=a+We&Mx 2duhYHmkk:+G7}WXXufuCV_An,J}Q__a:w@,CV:e&P%'|WXXufuCV_An,J}Q__a:I,CeT'bYWb}+D,B,::AuU_A 0000172339 00000 n +9s,BG} +++Wp}P]WP:YmbY _e WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d SR^AsT'b&PyiM]'uWl:XXK;WX:X 7|d*iGle e9rX%V\VS^A XB,M,Y>JmJGle Which of the above statements is/are correct ? Each sum is even. A. C,C,C,B1 4X{}uXX5b}[?s|JJXR?8&OiKJ,C,BxX8?X5 4XXXXch~JSXX5b_bm-NWXXKS\?S^O_u%!b!VS@m#_"b!*.Sy'Pq}XUR?s|JJXR?8: _!b!b!)/MsiOy=}XXXkIqu#B,**O922B,S@]_"b!*.Sy'Pq}XUR?s|JJXR?8B,B,BS^R)/z+!b!@ K:QVX,[!b!bMKq!Vl Hypothesis: Both numbers taken must be positive. The sum of any two consecutive integers is always odd. UyA >+B,b!pe?dV)+ #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e kPy!!!b}X_++a\ ] keywWXXcg\ ] KJE+B,B1 XB,_O_u%!VXXXX8+B,BA 4XXX.WXJ}XX B@q++aIqU *. >> |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s Determine whether the conjecture is true or false Dividing by 2 always produces a number less than the original number. Now, note that either $x$ is a multiple of $3$ or $(x^2+2)$ is a multiple of three. kLq!V>+B,BA Lb kLq!V>+B,BA Lb .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ >> "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ w *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* 44 0 obj A question of NUMBER THEORY and divisibility of 7. Find the smallest number. mrftWk|d/N9 MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie LwwvX,WyS18g]Qt'zi``{Xfo7=H8SS 0my*e| The smaller of two consecutive integers is eight less than A straightforward word problem solved using an equation. The conclusions obtained via inductive reasoning are only probable but not certain. endstream 0000058664 00000 n 0000058374 00000 n +9Vc}Xq- We solved the question! B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb 16060 S RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* Make a conjecture about the next number in the given sequence. #Z: *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 Answered: 7.2B 1. The sum of two consecutive odd | bartleby X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle sum of five consecutive integers inductive reasoningtraffic signal warrant analysis example. #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ kLq!V OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e &!t_j IYY~XbMXjf5XSWXQ__a}>+(\@kWX6YHUMM:~+D,jXUwbM@bMU_aEY~~pu!_!b2d"+CV66)!b-#VN5kV5UY~e&:W X~ejetY,BBvXu/!AY $TeVWWp_} <> =*GVDY 4XB*VX,B,B,jb|XXXK+ho 6XXX KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! cEV'PmM UYJK}uX>|d'b Create beautiful notes faster than ever before. e+D,B1 X:+B,B,bE+ho|XU,[s *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* kLq!V>+B,BA Lb mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ Inductive reasoning is a reasoning method that recognizes patterns and evidence from specific occurrences to reach a general conclusion. Which is the biggest integer that divides all integers that are the product of three consecutive odd numbers? mrJy!VA:9s,BGkC,[gFQ_eU,[BYXXi!b!b!b!b')+m!B'Vh+ sW+hc}Xi s,XX8GJ+#+,[BYBB8,[!b!b!BN#??XB,j,[(9]_})N1: s,Bty!B,W,[aDY X: KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! 6++[!b!VGlA_!b!Vl Solution List some examples and look for a pattern. 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ 2d@b U!B,Bz35UY3>++LPW~ZC,BO2dWQWZmmR!0,B,BLbMU! |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb stream endobj moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l Use inductive reasoning to form a conjecture. mrJy!VA:9s,BGkC,[gFQ_eU,[BYXXi!b!b!b!b')+m!B'Vh+ sW+hc}Xi s,XX8GJ+#+,[BYBB8,[!b!b!BN#??XB,j,[(9]_})N1: s,Bty!B,W,[aDY X: #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e
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