UyA Solution. 0000055055 00000 n 7|d*iGle 71 0 obj cEV'PmM UYJK}uX>|d'b 9b!b=X'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~-e&WXC,C!}e2d-P!P_!b!sUb!b!ez(p+ It is consistent with the above answer. wl|k^Mx rr,hlX_ CC.912.G.CO.11 Prove theorems about parallelograms. _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b ~+t)9B,BtWkRq!VXR@b}W>lE s 4XB,,Y endobj *. ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! 0000151388 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 *.*b BIB,BshlD}e+&X7>W@YYW'b 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 +9Vc}Xq- 0000053987 00000 n X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d So, the statements may not always be true in all cases when making the conjecture. Multiple Choice Which of the following is a counterexample of the conjecture below? 0000008821 00000 n Click here to get an answer to your question Induction proof for the sum of any five consecutive integers is divisible by 5 (without remainder). 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b *.*b Make and test conjecture for the sum of two even numbers. b"b!. 6XXX ,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 0000071968 00000 n *. ^[aQX e So, before that, we have to figure out two concepts: what is an integer? 16060 kLq!V>+B,BA Lb +9s,BG} wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U mX+#B8+ j,[eiXb kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! 6++[!b!VGlA_!b!Vl endobj *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD 2. UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb 35 0 obj *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe b9ER_9'b5 B,B, A question of NUMBER THEORY and divisibility of 7. 'bul"b 6++[!b!VGlA_!b!Vl m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> =++DceZ+C!k~u!!MxuM!nb!BI!VAuU_AE,w+h #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b ~iJ;WXX2B,BA X}+B,J'bbb!bUSbFJXXsNAub!b)9r%t%,)j? q++aIi *b!VBN!b/MsiU"2B,BA X+WXhg_"b!*.SyU_bm-R_!b/N b!:Oyq\U++C,B,T@B,j_@seeX5&r% +!b!b)O:'Pq}Xkk}X8SXKS\?Ubbb!b!Bb!VC,C,C,B1+a\ kNy'bl'bbb!b\ +JXXsN Tr_!b/9r%t%,)r_!b/N b!:Oy}uXXXX8ke}XkL|JXA,WBB,S@5u*O 7|d*iGle !}XXXGkfY}+(\T+(0Q_A{XHmWSe2dMW!C,BB _!b!b!CV_A e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX 12 0 obj Thus, answer choice C A+25 is correct. So if any one of the cases is false, the conjecture is considered false. cXB,BtX}XX+B,[X^)R_ #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ 9b!b=X'b The sum of any two consecutive integers is always odd. This type of reasoning forms a causal connection between evidence and hypothesis. Now we test this conjecture on another sequence to consider if the derived conclusion is in fact true for all consecutive numbers. >Q@kWW _!b X_=dd:eY* _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** 6XXX b 60 + 62 + 64 + 66 + 68 = 320. kLq!V B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb Sum of Five Consecutive Integers Calculator. <> 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: k^q=X cXB,BtX}XX+B,[X^)R_ *.R_%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 Now, note that either x is a multiple of 3 or ( x 2 + 2) is a multiple of three. mrJyQ1_ |d/N9 :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e 6XXX This inductive method draws conjecture from similar qualities or features of two events. cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X endobj XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** Let us take into consideration the integer numbers. >S?s|JJXR?B,B,B,W?)u.o*kaq!WX.O922B,m_5%+aXX5BB,Bxq++aIi ~+B,'bu <> b=Ju_=`XXXXb_=XyMU|JXX+"22'+Msi$b"b!b5I4JJXAWzz:'Pqq!b!b!V_"b!VJ,C>Kg\ 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_ For example, test that it works with . endobj 20 C. 12 D. 30 E. 56 16. . As $3x(x^2+2)$ will have a multiple of three occurring once in the $3$, and once in either the $x$ or the $(x^2+2)$ term, we have that the sum of three consecutive cubes is a multiple of nine. )+B,:(Vh+LWP&VW|k^MxmM]7WYYzu!pbqXXGU'bM 0000161836 00000 n k~u!R_ApV" moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l endobj 'bu 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. 16060 s 4Xc!b!F*b!TY>" *. 'bul"b #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe +++LWe!!+R@fj*Y2d^@{WX5Xb!b!bMR!0Q_A&j *.vq_ e e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& m,b}lXGU'bM _TAXXWWeeUA,C,C,B,ZXTs|XX5k9*|XiJXX5J}XX B@q++aIqYU 0000151681 00000 n cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ _)9r_ N=2d" Yu!>+BB,ZT@uh}2dY_A{WWp}P]U'b} Y Divisibility of consecutive natural numbers. SZ:(9b!bQ}X(b5Ulhlkl)b The sum of two consecutive integers is 5, what are the integers? =*GVDY 4XB*VX,B,B,jb|XXXK+ho m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> '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 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: 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 B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb kMuRVp7Vh+)Vh+L'b : >_!b9dzu!VXqb}WB[!b!BI!b5We b"bu#VCXXX/-9r%_b!b!b,N T B| }XXbbb!b#VBJXXJ+ZXiJXX&bu !VJ|eXX8S Xj2k~$b"b!bm,O92z+MrbV+E_ c++D,CCY,CV_YY~5:H_!b!bRC_a(_0,BB2dN=:a*_Y Number 20 ends with 0. *. KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! endobj mB&Juib5 XXXKXXXX [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** 8 0 obj *|eeU+C,B,zb!b!Vqy!!!}_!+a\ ] +JXXS|XXX+g\ ] K|eXX8SbbUWXXH_5%V/,B,BC,C,CB,W"bV #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb Where does this (supposedly) Gibson quote come from? _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl 2. N=2d" Yu!_!b!b-N :AuU_MQ_=++LWP>>[[S WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d |d/N9 $$(3k + 1)((3k + 1)^2+5)=(3k + 1)(9k^2+6k+6)=0 \mod 3$$, KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb 'b k^q=X kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu So, about 70% of doves are white. endobj by Sum of Consecutive Integers Word Problems. 0000057079 00000 n 0000058664 00000 n OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e There are 10 consecutive nonzero positive integers. mX8@sB,B,S@)WPiA_!bu'VWe }JT'bY@f kByQ9VEyUq!|+E,XX54KkYqU mX8@sB,B,S@)WPiA_!bu'VWe 0000071114 00000 n 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e 0000136995 00000 n where a 1 - first term d is the common difference Types of Consecutive Integers Depending upon the type of integer, the different types of consecutive integers are as follows: Odd Consecutive Integers Even Consecutive Integers Positive Consecutive Integers mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s >> *.N jb!VobUv_!V4&)Vh+P*)B,B!b! Although it looks a bit similar, there are still differences. K:QVX,[!b!bMKq!Vl The difference between inductive reasoning and deductive reasoning is that, if the observation is true, then the conclusion will be true when using deductive reasoning. Make a conjecture about the next number in the given sequence. ?*'++a\ B *.F* endobj *.*R_ #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb As we can see this pattern for the given type of numbers, lets make a conjecture. SZ:(9b!bQ}X(b5Ulhlkl)b +9Vc}Xq- 'bu :XIWSXWXE22 !!b!_vB,B,*.O90 0000053452 00000 n +9Vc}Xq- endobj 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 Inductive reasoning, because a pattern is used to reach the conclusion. Answer (1 of 4): let x-2,x-1,x,x+1,x+2 are 5 consecutive integers sum is -5 soo =>x-2+x-1+x+x+1+x+1 =-5 =>5x=-5 => x=-1 x-2 = -3 x-1 = -2 x+1 = 0 x+2 = 1 therefore numbers are In this tutorial, you learned how to sum a series of consecutive integers with a simple and easy to remember equation. WP,[a(w,Bsj(L_!b}:!!+R@N Kj*TT'bY@B,B:*VXp}P]WPM`e Consider 2 and 5. UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV :X +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk KbRVX,X* VI-)GC,[abHY?le KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe 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 [++LBI $(+C!kYHu!_!b!G|XXB,,J}&E}W"__aX~'bMj WV]Ji_Ye2dEh ,[s #4GYc!,Xe!b!VX>|dPGV{b _)9r_ mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab m% XB,:+[!b!VG}[ endobj S: s,B,T\MB,B5$~e 4XB[a_ :X]e+(9sBb!TYTWT\@c)G *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b endobj qWX5 B:~+TW~-b&WN}!|e5!5X,CV:A}XXBJ}QC_a>+l0A,BeTUW,CxbYBI!Cb!b *GY~~_aX~~ b"VX,CV}e2d'!N b=X_+B,bU+h VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb kLq!V>+B,BA Lb k^q=X Sum of Five Consecutive Integers Video. *Vs,XX$~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 (By adding one more to the previous number you will get the next consecutive integer.) mrftWk|d/N9 Example: Prove the sum of two odd numbers is an even number. ^[aQX e ?l >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ 63 0 obj <> 'b *. ~+t)9B,BtWkRq!VXR@b}W>lE So the numbers are 18, 19, 20, 21, 22 and statement 1 is correct. Converse: If a number is a whole number, then it is a natural number KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb kaqXb!b!BN d+We9rX/V"s,X.O TCbWVEBj,Ye b 4IY?le 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 0000149215 00000 n HT{PG| A|0P#kQbJQ,UD`'DTb qZ*0 XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** *.vq_ 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! *.R_ 'b &&e?d"bCV)!,B}Wpu!_!b2d2dR IYY~X+B,BU:~+(~_+(\@kWX6YYTmmRC_!b!V;* WP>+(_X/WeXuLukkY #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d cXB,BtX}XX+B,[X^)R_ *. *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 *.R_ From the above, we can observe that the answer of all the sums is always an even number. kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu kSu!R_Anb!VHYB[a(w,. 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ kLq!V 'bu +C,,Hmkk6 X}_ 0000152179 00000 n *. _)9r_ 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: 34 0 obj XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** BNxmMY Case $3: x=3k+2$, then $x^2+2=9k^2+12+4+2=3(3k^2+4k+2)$. +DYHeO,C!+R@5):X_!b!R_A{WWp_WW _!bee2dE:W,CxbYBI! *. 6++[!b!VGlA_!b!Vl #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 'bu |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s *.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, You can make the following conjecture. endobj *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* |d/N9 !*beXXMBl b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ In this tutorial, you learned how to sum a series of consecutive integers with a simple and easy to remember equation. 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 Use inductive reasoning to show that the sum of five consecutive integers . Proof: x = 3 k x 0 ( mod 3) Hence, the conjecture is false. :e+We9+)kV+,XXW_9B,EQ~q!|d *. 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We 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. [+|(!!kY X,CV65XWX&X e+D,B,ZX@qb+B,B1 LbuU0R^Ab 53 0 obj #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ ,B&PY+C!kYW'b #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, k d+We9rX/V"s,X.O TCbWVEBj,Ye 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). [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 b 4IY?le 64 0 obj |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s #T\TWT\@W' e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e sum of five consecutive integers inductive reasoning. *.vq_ N bU+(\TWbe+&+h|N|B,::!!+R@nZ That is, the sum of 5 consecutive even numbers is equal to 5 times the third even number. We noticed that, starting with 3, every second number can be written as a sum of two consecutive numbers; starting with 6, every third number (6, 9, 12 . :X 34 What is the third number? e+D,B1 X:+B,B,bE+ho|XU,[s mX+#B8+ j,[eiXb 5 weeks 6 days pregnant ultrasound pictures Projetos; is luke marrs adopted Blog; thomas aquinas natural law pdf Quem somos; . _WX B,B,@,C,C 34 K:QVX,[!b!bMKq!Vl 72 0 obj UyA ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb 0000117474 00000 n <> wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U <> endstream #T\TWT\@W' cEV'PmM UYJK}uX>|d'b mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L |d/N9 B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX 0000074950 00000 n *. ,X'PyiMm+B,+G*/*/N }_ 0000172525 00000 n #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G '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 ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU ,[s 2. <> Sum of the smaller and twice the larger is -4. 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 anschutz canada dealer. |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb Find a counterexample for: All even numbers are composite. . ,Bn)*9b!b)N9 Save my name, email, and website in this browser for the next time I comment. cEZ:Ps,XX$~eb!V{bUR@se+D/M\S OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e 0000006154 00000 n The general unproven conclusion we reach using inductive reasoning is called a conjecture or hypothesis. kPy!!!uWmT9\ ] +JXXskWX :e+We9+)kV+,XXW_9B,EQ~q!|d We Select the smallest value of P that satisfies given conditions. #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, b9ER_9'b5 #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe *. endobj Write 1245 as the sum of ve consecutive integers. KJkeqM=X+[!b!b *N ZY@b!b! *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* +DHu!!k%2d(eJ(B_!b!b=Xw+h *.vq_ XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X ?l Sum of five consecutive numbers equals . s 4XB,,Y _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** *. b"b=XQ_!b!b!b}pV'bujB*eeXXM|uXXXhZB%JSXr%D,J4KXg\ WJ|eXX8S6bu !!VK4 7WWX=++LT'bY@fj*YC,C!+R@N C_#;5UY~ Xg&PJ,CV:e&PB,B,B9 GY}+We&Mx3}5XNu!!MxmM]W'b$'}XXXs(_T 49 0 obj <> 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 kLq!VH :X m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L !V2 rev2023.3.3.43278. x 1 (x 1 1) 1 (x 1 2) 1 (x 1 3) 1 (x 1 4) 5 __?__ 22. <> <> :X\ :XXab]b!V*eeXU=_vB,B,*.O9Z>+BJSXr%D, e+D,B,ZX@qb+B,B1 LbuU0R^Ab 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: b9ER_9'b5 mX+#B8+ j,[eiXb endobj + '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 kLq!V>+B,BA Lb mrk'b9B,JGC. endstream 7|d*iGle The sum of three consecutive integers is 6++[!b!VGlA_!b!Vl S 'bul"b Are inductive and deductive the same type of reasoning? 'b hW1mieHQ%Q"2nHpvWuGZdU$m(%ErF [96 What is a word for the arcane equivalent of a monastery? VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ kaqXb!b!BN W+,XX58kA=TY>" :X 6XXX W+,XX58kA=TY>" &a_!bN bU+(\TW b9ER_9'b5 SR^AsT'b&PyiM]'uWl:XXK;WX:X 9b!b=X'b ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ 0000151930 00000 n <> Does ZnSO4 + H2 at high pressure reverses to Zn + H2SO4? S"b!b A)9:(OR_ b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# 14. 3. 7|d*iGle 48 0 obj +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe ):Ww+w,(!um;WYYhlX}X5:kRUp}P]WP}_+Vh+LWeXuN :X]e+(9sBb!TYTWT\@c)G 1 5, 1 6, 1 7, 1 8, 1 9. I appreciate it, We've added a "Necessary cookies only" option to the cookie consent popup. ,|Bc^=dqXC,,Hmk mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab k B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ Then the numbers are x, x + 1, x + 2, x + 3, and x + 4. _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L <> kN}Q__a}5X*0,BBet*eM,C!+R@5)ZFb!b!b=++LtVe&WWX]bY\eYe2dE&XB,B,B9GY~~nPb,B U})E}e+e+|>kLMxmMszWUN= |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb 0000072332 00000 n 0000002705 00000 n +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU m5XSYBB,B1!b%+B,GYB[a:_ V,rr&P[}N'CCte _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L 0000128573 00000 n [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* 4GYc}Wl*9b!U 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 s 4XB,,Y _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L KbRVX,X* VI-)GC,[abHY?le KVX!VB,B5$VWe 0000075143 00000 n *.*R_ 2 is an even number but not composite, as it is a prime number. 5. 16060 cEV'PmM UYJK}uX>|d'b 6XXX mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s +C,,Hmkk6 XloU'bM 35 0000136972 00000 n ,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+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX *. Find two consecutive positive integers whose product is 240. e *.*b <> UyA ,X'PyiMm+B,+G*/*/N }_ w$TeVWWO @b6!kYHu!_!b!VX+B,B5 JYY~ + log(x1)log(x+2)=log(x+2)log(x1). Everything you need for your studies in one place. K:QVX,[!b!bMKq!Vl I. Download Free PDF Download PDF Download Free PDF View PDF. mX8@sB,B,S@)WPiA_!bu'VWe True/False: What is the answer to the conjecture? UyA MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX [5_bn~3;D+dlL._L>; ,S=& endstream endobj 365 0 obj <>stream mrk'b9B,JGC. *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 31 0 obj mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s R22 !!b!b5+/,B,BC,CC_!xb)UN,WBW Contrapositive: If a number is not a whole number, then i is not a natural number mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s cEZ:Ps,XX$~eb!V{bUR@se+D/M\S XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X k~u!AuU_Ajj,*VX=N :>6'b9d9dEj(^[S n+Vzu!|J i_a:kYu!V@e+L(++B,7XS5s*,BD}&E}WN5+D,C!kxu)}e&&e ^[aQX e 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! #Z: mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab 9b!b=X'b +9Vc}Xq- ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! endobj mrftWk|d/N9 4GYc}Wl*9b!U 4GYc}Wl*9b!U B,Bs&eWP>+ 46 0 obj Make a test a conjecture about the sum of any three consecutive integers. 0000172446 00000 n 6XjBwj?+WBWA X++b!V)/MsiOyiJK #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb b9ER_9'b5 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: Conversely, deductive reasoning is more certain and can be used to draw conclusions about specific circumstances using generalized information or patterns. SR^AsT'b&PyiM]'uWl:XXK;WX:X Lets once again take a look at what we learned through examples. m%e+,RVX,B,B)B,B,B LbuU0+B"b Create the most beautiful study materials using our templates. #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ |d/N9 k^q=X Do}XXXXKJ,Ckaq=X?b!b!Vqy!!!b$_$++a\ kNyWXX3W%Xo #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! stream *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe XXXSXXX22B,BUSbB,B,*.O922jJbMMbVtWXXB,B!b!b!}bbbUvWMNBI,WBW To find the true conjecture from provided information, we first should learn how to make a conjecture. +GY~W~~1e"!kMu!S;|e2d:~+D XWXXuWX=:Wx +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk )#j(^[S MxmM]W'FN b!bR@zg_ ,X'PyiMm+B,+G*/*/N }_ |d/N9 Now, note that either $x$ is a multiple of $3$ or $(x^2+2)$ is a multiple of three. 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U A:,[(9bXUSbUs,XXSh|d |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! ,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 50 0 obj k *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe KJkeqM=X+[!b!b *N ZY@b!b! e e+D,B1 X:+B,B,bE+ho|XU,[s cB WX+hl*+h:,XkaiC? cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ Inductive reasoning is considered to be predictive rather than certain. 0000144950 00000 n #T\TWT\@W' log(x+2)log(x1)=log(x+2)log(x1)\frac { \log ( x + 2 ) } { \log ( x - 1 ) } = \log ( x + 2 ) - \log ( x - 1 ) # XGV'b_!b!BC+(\TW= "T\TWbe+VWe9rXU+XXh|d*)M|de+'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 X2dU+(\TW__aX~We"V65oW,C!^@{e+D,Z+B,W'bMUp}P]Fb&WN}Q_!bEj(^[S;o{e2d X,BBBI*_aKY~~ wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U S: s,B,T\MB,B5$~e 4XB[a_ K:'G #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe s 4XB,,Y 6XXX W+,XX58kA=TY>" stream For example, the sum of 3 consecutive odd integers is 30, find these odd integers. XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X endobj C,C,C,B1 X}uXX5b}[?s|JJXR?86B,B,B>S^R)/z+!b!N 0000003548 00000 n cEZ:Ps,XX$~eb!V{bUR@se+D/M\S Trying to understand how to get this basic Fourier Series. 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ 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 stream q!V[22B,B X+[+B 4XXXXc+W That is, suppose that each number is either a multiple of $2$ or $3$. kLq!VH *.)ZYG_5Vs,B,z |deJ4)N9 ,[s Truth value: True. 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 cEZ:Ps,XX$~eb!V{bUR@se+D/M\S sum of five consecutive integers inductive reasoning sum of five consecutive integers inductive reasoning. |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s 0000144927 00000 n |d/N9 KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! Then state the truth value 43 0 obj ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l *.)ZYG_5Vs,B,z |deJ4)N9 MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe e So our conjecture is true for all even numbers. XXXMl#22!b!b *n9B,B,T@seePb}WmT9\ ] +JXXsWX mB&Juib5 K:'G :XW22B,BN!b!_!bXXXXS|JJkWXT9\ ] +JXb!b!bu * W+,XX58kA=TY>" mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s +++LtU}h &!t_}W[SSH+D,jXeb-X'bj *,BD[}P]WP:YmbYNw5e:,BBvUg?Y@udm k 0000005489 00000 n 'bul"b x+*00P A3S0i wI ,[s WX+hl*+h:,XkaiC? NgkY KJkeqM=X+[!b!b *N ZY@b!b! ~iJWXX2B,BA Xm|XXhJ}J++!b!b,O:WXkOq!V22!b!b *N j+B,T@seeXU+W\ ] keyB,B=3W%X|XX{:Xu4!!VkPq!V_!b!C,C,C,BR_F|JJXX+Nb!b)9r%t%,)j+B,S@)B)un*|eXX >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s The smaller of two consecutive integers is eight less than A straightforward word problem solved using an equation. NX~XXV'P>+(\CQ_Z+|(0Q@$!kY+2dN=2d" ) Consider the true statements Numbers ending with 0 and 5 are divisible by 5. U}/E}e+|(V;V: 4 0 obj Here, the statements are true, but the conjecture made from it is false. A simple example of inductive reasoning in mathematics. 'bub!bC,B5T\TWb!Ve s 4Xc!b!F*b!TY>" s 4XB,,Y ~+t)9B,BtWkRq!VXR@b}W>lE #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb ,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 m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> x+*00P A3S0i wR ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk Let E be the set of even numbers (in U). mrs7+9b!b Rw 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!@ b 4IY?le b 4IY?le Suppose x and y are odd integers. 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
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sum of five consecutive integers inductive reasoning