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Observe: We see the sequence is increasing. S 1 5, 1 6, 1 7, 1 8, 1 9. $$(3k + 1)((3k + 1)^2+5)=(3k + 1)(9k^2+6k+6)=0 \mod 3$$, cB kLq!V>+B,BA Lb *.F* Let x, x+2, x+4 and x+6 be the four consecutive odd integers. KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb ,[s ,Bn)*9b!b)N9 A:,[(9bXUSbUs,XXSh|d Sum of the smaller and twice the larger is -4. *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> +"b!Bu+B,W'*e 56 0 obj cEZ:Ps,XX$~eb!V{bUR@se+D/M\S 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe _)9r_ #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X e |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s *. Let us take into consideration the integer numbers. However, inductive reasoning does play a part in the discovery of mathematical truths. # 4bWSulBB,b!GYB[aeC_ VBj(^WB5:VXXJ;XXXcB,J4WX+(\_A{e++Q@+[aTae!b!VXYY7WST\Y&Xu^b!b!b!Fb *. A simple example of inductive reasoning in mathematics. SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G >> stream +M,[; 0000152370 00000 n 'bu 26 0 obj GV^Y?le The different types of inductive reasonings are categorized as follows: This form of reasoning gives the conclusion of a broader population from a small sample. 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ 4. Express the fraction 164 using negative exponent. mrs7+9b!b Rw S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G Thus, answer choice C A+25 is correct. 4GYc}Wl*9b!U 'bu So, we can use 2 * N + 1 to represent the first integer, then the remaining 3 consecutive odd numbers can be represented as 2 * N + 3, 2 * N + 5, 2 * N + 7 and 2 * N + 9. X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl 34 |d/N9 endobj >> e9rX%V\VS^A XB,M,Y>JmJGle *.*b bbb!b!)z~a!b!b'bbb|X}uXr%D,B9]b!b!bu)9r%t%,iAXXi_=XXX22B,BUSbB,B,*.O922 *. 8 0 obj Caution: It is not always the case that the conjecture is true. cB *.R_ cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ Conjecture: All quadrants of a circle are being filled with color in a clockwise direction. ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu #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 S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu e+D,B,ZX@qb+B,B1 LbuU0R^Ab _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** cXB,BtX}XX+B,[X^)R_ 14. ,[s 45 0 obj *.F* s 4Xc!b!F*b!TY>" endstream <> Suppose x and y are odd integers. KVX!VB,B5$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 B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b *.R_%VWe 'b,N Z=_=Xy!!!b!BbmwyN $}Xq++aIi B]byiK4#_!b!VB X+'+O922B,S@{B !b.O:'Pqyb!V)/MsiOyiJK+B,j^@8ke|b 4XXXXcVvW!B T\^S*.O:'uW_bm-N ZE_!OyiJKKS\?'|XXcV'b|X)O922B,S@B !b.O:'Pqy*9r%t%,)Z@ e+D,B1 X:+B,B,bE+ho|XU,[s 15,\,16,\,17,\,18,\,19 15, 16, 17, 18, 19. Then use deductive reasoning to show that the conjecture is true. wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U *.*R_ mrftWk|d/N9 0000008844 00000 n !*beXXMBl B,B,R@B,B,BI What is an advantage of using inductive reasoning? By using our site, you :e+We9+)kV+,XXW_9B,EQ~q!|d mB&Juib5 Sum of Five Consecutive Integers Video. ,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 &!t_}W[SSH+D,jXeb-X'bj *,BD[}P]WP:YmbYNw5e:,BBvUg?Y@udm k WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d H\$56Nkxd}AnT?6P]H1DMa #" cB *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe Nie wieder prokastinieren mit unseren Lernerinnerungen. .) 'b mX8@sB,B,S@)WPiA_!bu'VWe nb!Vwb s 4XB,,Y |WxD~e"!:Ue+C $Pe*+D,BFW _;GY mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! *.*b *.R_%VWe *Vs,XX$~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 s 4Xc!b!F*b!TY>" W+,XX58kA=TY>" 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 :X]e+(9sBb!TYTWT\@c)G S"b!b A)9:(OR_ stream SR^AsT'b&PyiM]'uWl:XXK;WX:X stream B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX 0000158742 00000 n 0000117474 00000 n 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe 29 0 obj What is the symbolic form of and inverse statement? ,X'PyiMm+B,+G*/*/N }_ 'bub!bC,B5T\TWb!Ve 2 is an even number but not composite, as it is a prime number. +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> b) Illustrate how the two algorithms you described in (a) can be used to find the spanning tree of a simple graph, using a graph of your choice with at least eight vertices and 15 edges. mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G A:,[(9bXUSbUs,XXSh|d endstream *. b. Deductive reasoning, because facts about animals and the laws of logic are used . 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: 'b 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ kPy!!!b}X_++a\ ] keywWXXcg\ ] KJE+B,B1 XB,_O_u%!VXXXX8+B,BA 4XXX.WXJ}XX B@q++aIqU knXX5vOy=}XXbbb!b!D b 4IY?le |d/N9 x+*00P A3S0i w C,C,C,B1 X}uXX5b}[?s|JJXR?86B,B,B>S^R)/z+!b!N Truth value: True. We k^q=X e9rX |9b!(bUR@s#XB[!b!BNb!b!bu To subscribe to this RSS feed, copy and paste this URL into your RSS reader. 9b!b=X'b stream K:QVX,[!b!bMKq!Vl KbRVX,X* VI-)GC,[abHY?le *. ,X'PyiMm+B,+G*/*/N }_ b9ER_9'b5 We *.N jb!VobUv_!V4&)Vh+P*)B,B!b! moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l XbbbUn++W5USbB,B,*.OB!lb)UN,WBW wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U |d/N9 SR^AsT'b&PyiM]'uWl:XXK;WX:X Example 1. ~+t)9B,BtWkRq!VXR@b}W>lE SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G That is, the sum of 5 consecutive even numbers is equal to 5 times the third even number. *.R_%VWe #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b b ANSWER The sum of any two odd numbers is even. KbRVX,X* VI-)GC,[abHY?le kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu 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. 0000058664 00000 n Sign up to highlight and take notes. mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle k &4XS5s*,BDW@kWX5TY,CN!V@uWXQb!b=X_+B,@bMU! k kLq!V #T\TWT\@W' 55 0 obj Six consecutive integers equal 27 when added together. 2021-04-26. 4&)kG0,[ T^ZS XX-C,B%B,B,BN 7|d*iGle 'Db}WXX8kiyWX"Qe kLq!VH Sum of five consecutive integers x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 5x + 10 Five consecutive integers always are equal by five. *.R_ mrftWk|d/N9 S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu 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 WP}_o$Te *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe SZ:(9b!bQ}X(b5Ulhlkl)b #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b Determine whether the conjecture is true or false Dividing by 2 always produces a number less than the original number. 35 B. 34 e !*beXXMBl #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s s 4Xc!b!F*b!TY>" 0000068633 00000 n kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu kLq!V>+B,BA Lb 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b <> #4GYc!,Xe!b!VX>|dPGV{b e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX 0000066194 00000 n e #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 [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 e endobj That is, the sum of 5 consecutive even numbers is equal to 5 times the third even number. *.vq_ Make a test a conjecture about the sum of any three consecutive integers. k~u!l *.R_ XW+b!5u]@K 4X>l% T^\Syq!Bb!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 W/?o *R_A{WWNg_ m% XB,:+[!b!VG}[ mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle vkYe&+(Oo~>+(\@kWX5TY,C SInce there are 5 integers, 5x5 would make the sum 25 greater than A. *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! s 4XB,,Y Solution for 7.2B 1. 'Db}WXX8kiyWX"Qe Inductive reasoning is a reasoning method that recognizes patterns and evidence from specific occurrences to reach a general conclusion. 50 0 obj U}#*+[aXw+h|B,:XY}XuC,,[a65XsWT'bY]Si_!bNU d+We9rX/V"s,X.O TCbWVEBj,Ye 9b!b=X'b W+,XX58kA=TY>" 0000151681 00000 n mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ I thought of doing a proof by contradiction. e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b m% XB,:+[!b!VG}[ Arccsc Calculator Find the Exact Value of Inverse Cosecant, Arcsec Calculator Find the Exact Value of Inverse Secant, Arccot Calculator Find the Exact Value of Inverse Cotangent, Arctan Calculator Find the Exact Value of Inverse Tangent, Inverse Cosine Calculator Find The Exact Value of Arccos, Inverse Sine Calculator Find The Exact Value of Arcsin, Inverse Trigonometric Functions Calculator, Trigonometric Functions Conversion Calculator, Trig Calculator Find 6 Trigonometric Functions by Angles or Sides, Sum of Four Consecutive Integers Calculator, Sum of Three Consecutive Integers Calculator, Sum of Two Consecutive Integers Calculator. 0000144927 00000 n "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu JSXr%|0B,B,B,B,z@N T\?c|eXX5wj5UWbbEeeuWO VR)/Ir%D,B,;}XXLb)UN,WBW +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk *. #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b SR^AsT'b&PyiM]'uWl:XXK;WX:X *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 bbb!6bTX?JXX+ B'+MrbV+N B,jb!b-)9I_"O+C,B,B @bXC*eeX+_C?3XXXh =*GVDY 4XB*VX,B,B,jb|XXXK+ho #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ So, the given conjecture is false. <> 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe 0000056695 00000 n sum of five consecutive integers inductive reasoning. e D:U!_;GY_+ZC,B e Z 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: #Z: +|AuU_Az&Y |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb Its 100% free. So $n = 21$.} d+We9rX/V"s,X.O TCbWVEBj,Ye p}P]U'b!bb9d MxmM=&Pu:VXXkg?W>B Set individual study goals and earn points reaching them. WSB3WXXX+WX+B,C,Cr%$b"b!bm,R_!b!VJSXr%D/ w <> endobj endobj Given that $a$, $b$, $c$ are natural numbers, with $a^2+b^2=c^2$ and $ c-b=1$, prove the following. So if any one of the cases is false, the conjecture is considered false. endobj hW1mieHQ%Q"2nHpvWuGZdU$m(%ErF [96 s 4XB,,Y |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, S"b!b A)9:(OR_ mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe *. X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We ~+t)9B,BtWkRq!VXR@b}W>lE So, before that, we have to figure out two concepts: what is an integer? By registering you get free access to our website and app (available on desktop AND mobile) which will help you to super-charge your learning process. *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* <> kByQ9VEyUq!|+E,XX54KkYqU let a and b be 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: ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ k mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! [++LWe!!+R@zoeZ,C X~X+B,::I9dp}P]5Ww0A,w+hMxmM!*CVX,CV:@bAXXV'35UY3fNb&WN}Qb" ~Yse2dEh #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl <> [ b65CVKi_9d9dN="b!^J &a_!bN bU+(\TW s 4Xc!b!F*b!TY>" mrs7+9b!b Rw endstream GV^Y?le 'bu _b!b!b,b_!b!VJ,Cr%$b"b!bm,R_!b!VJSXr%|+B,XX+P\J2 +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG 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 k~u!AuU_A4"_;GY~~z&Ya_YhYHmk #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ * SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- mrs7+9b!b Rw *.*b 2.1 Use Inductive Reasoning Big Idea: To use INDUCTIVE REASONING in mathematics. m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** _TAXX+uWXX5 )_a:kY5!V@e+L(++B,7XS5s*,BD}VE}WN5+D,C!kxuY}e&&e b 4IY?le 'b +GY~W~~1e"!kMu!S;|e2d:~+D XWXXuWX=:Wx a. endobj 65 0 obj e9rX%V\VS^A XB,M,Y>JmJGle kSu!R_Anb!VHYB[a(w,. XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** 0000053428 00000 n Find the next number in the sequence 1,2,4,7,11 by inductive reasoning. *. #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ For example: What is the sum of 5 consecutive even numbers 60, 62, 64, 66 and 68? ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B Inductive reasoning uses previous examples and patterns to form a conjecture. m mrs7+9b!b Rw U}WCu XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> *. :X]e+(9sBb!TYTWT\@c)G 11 0 obj 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 [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 You have then the sum of three consecutive cubes is $(x-1)^3+x^3+(x+1)^3 = 3x^3+6x=3x(x^2+2)$. 0000004910 00000 n b"b=XQ_!b!b!b}pV'bujB*eeXXM|uXXXhZB%JSXr%D,J4KXg\ WJ|eXX8S6bu !!VK4 #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 6 0 obj 0000002705 00000 n Then use deductive reasoning to show that the conjecture is true. So the numbers are 18, 19, 20, 21, 22 and statement 1 is correct. b nb!Vwb 0000125414 00000 n This inductive reasoning predicts a future outcome based on past occurrence(s). _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** KbRVX,X* VI-)GC,[abHY?le =*GVDY 4XB*VX,B,B,jb|XXXK+ho !*beXXMBl b9ER_9'b5 G50j*aT endstream mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab [+|(>R[S3}e2dN=2d" XGvW'bM d+We9rX/V"s,X.O TCbWVEBj,Ye WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d 17 0 obj This type of reasoning forms a causal connection between evidence and hypothesis. moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l 0000161836 00000 n >> endstream 63 0 obj |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s Step 3 Test your conjecture using other numbers. S %PDF-1.4 % % kMuRVp7Vh+)Vh+L'b : >_!b9dzu!VXqb}WB[!b!BI!b5We *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 We solved the question! b"b! <> *.*b which marvel character matches your personality. 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. mrftWk|d/N9 d+We9rX/V"s,X.O TCbWVEBj,Ye +DYY,CVX,CV:kRUb!b!bZ_A{WWx 0000005784 00000 n mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& s 4XB,,Y Show all of your work.