sum of five consecutive integers inductive reasoningwhat happened to mark reilly strong island
s 4Xc!b!F*b!TY>" +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- mX8@sB,B,S@)WPiA_!bu'VWe #T\TWT\@W' 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 What sort of strategies would a medieval military use against a fantasy giant? kLq!V>+B,BA Lb +9s,BG} 9b!b=X'b SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab K:QVX,[!b!bMKq!Vl Show all of your work. I also have seen white geese there. e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e 'b wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U (By adding one more to the previous number you will get the next consecutive integer.) 1. !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe Using the formula to calculate, the third even integer is 64, so its 5 times is 5 * 64 = 320, the answer is correct. k^q=X m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L *. *.F* &XbU3}5v+(\_A{WWpuM!5!}5X+N=2d" W'b_!b!B,CjY}+h "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu *. kLqU +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b |d/N9 16060 6XjH7|Xq++aIi B]byiK4XOb!bV'b@kLq! 9b!b=X'b q!Vl GY~~2d}WO !N=2d" XGv*kxu!R_Ap7j(nU__a(>R[SOjY X,CV:nb!b!b! Short story taking place on a toroidal planet or moon involving flying. kxu!B,B,Z,J}Q_0,BB2dN=:d5|e2d:~+D XG b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! Inductive reasoning, because a pattern is used to reach the conclusion. ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U 0000006092 00000 n B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX KJkeqM=X+[!b!b *N ZY@b!b! cXB,BtX}XX+B,[X^)R_ k 0000073873 00000 n >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ Sum of Five Consecutive Integers Calculator. +R@Y/eZ,C X,BBBI*f,BD}Q_!bEj(^[S!C2d(zu!!++B,::kRJ}+l)0Q_A{WX Y!@YhY~Xi_!b!9 X2dU+(\TW_aKY~~ *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- [+|(>R[S3}e2dN=2d" XGvW'bM K:QVX,[!b!bMKq!Vl sum of five consecutive integers inductive reasoningfood taboos in yoruba land. #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl 'b ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl _)9r_ kLq!V ~iJ[WXX2B,BA X;_!b!VijJ,W\ kNy}XXBN!b/MsqUWXX58knb!bh*_5%+aXX5HB,Bxq++aIi ~+^@)B)u.nj_bbU'bB,Bty!!!b!}Xb"b!*.Sy, :e+We9+)kV+,XXW_9B,EQ~q!|d 3 0 obj 21 0 obj <> e 2eYN5+D,jeT' *C $Pe+k #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b We 2. S: s,B,T\MB,B5$~e 4XB[a_ e+D,B1 X:+B,B,bE+ho|XU,[s m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> endobj That is, the sum of 5 consecutive even numbers is equal to 5 times the third even number. KbRVX,X* VI-)GC,[abHY?le 0000054170 00000 n b"b! Inductive reasoning sequence example, Mouli Javia - StudySmarter Originals. :e+We9+)kV+,XXW_9B,EQ~q!|d +++Wp}P]WP:YmbY _e e9rX |9b!(bUR@s#XB[!b!BNb!b!bu |d/N9 e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX be_@{e2dEj(^]SuW'bM m%e+,RVX,B,B)B,B,B LbuU0+B"b K,C!+},C!k6YHu!k(^b!b!b=++LtVe&WWX]bY\eYe2dE&X!_!b!b! K:QVX,[!b!bMKq!Vl 6XXX +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG ?l ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ endobj 'bub!bC,B5T\TWb!Ve VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* . mrs7+9b!b Rw KbRVX,X* VI-)GC,[abHY?le KJkeqM=X+[!b!b *N ZY@b!b! *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* mX+#B8+ j,[eiXb mX+#B8+ j,[eiXb Inductive Reasoning - PDFs. Choose the correct conjecture for the following? X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 stream *.*b 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk 34 *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- _b!b!b,b_!b!VJ,Cr%$b"b!bm,OR_!b!VJSXr%JO endobj 0000117497 00000 n 6++[!b!VGlA_!b!Vl =*GVDY 4XB*VX,B,B,jb|XXXK+ho GV^Y?le kLq!V>+B,BA Lb e+D,B,ZX@qb+B,B1 LbuU0R^Ab ,Bn)*9b!b)N9 6++[!b!VGlA_!b!Vl endstream kLq!V *.R_%VWe mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe wV= e mB&Juib5 For example: What is the sum of 5 consecutive even numbers 60, 62, 64, 66 and 68? But the chosen numbers 2 and 5 are not positive. b"b!. KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! A conjecture is said to be true if it is true for all the cases and observations. e+D,B,ZX@qb+B,B1 LbuU0R^Ab 'bu #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb 'b *.N jb!VobUv_!V4&)Vh+P*)B,B!b! 'bu k^q=X mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** 0000151746 00000 n 'bul"b 0000075143 00000 n ^[aQX e endobj \end{align*}, This can be used to deductively prove that the sum of cube of $3$ consecutive numbers is divisible by $3$ but I can't prove it is divisible by $9$. 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! b"b!:*b!b53W%uT+B,jb!b!b =+C,C 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu 0000072332 00000 n *. k^q=X *.R_%VWe 'bul"b kByQ9VEyUq!|+E,XX54KkYqU *.vq_ *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu ,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 b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# C,C,C,B1 X}uXX5b}[?s|JJXR?86B,B,B>S^R)/z+!b!N b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# q!V[22B,B X+[+B 4XXXXc+W #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe 35 0 obj :X\ :XXab]b!V*eeXU=_vB,B,*.O9Z>+BJSXr%D, Conjecture: The sum of the first n odd positive integers is __?__. cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. *. ,X'PyiMm+B,+G*/*/N }_ mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab >> kLq!V>+B,BA Lb Whereas, deductive reasoning is called the "Top-Down" approach as its draws conclusions about specific information based on the generalized statement. B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb *. 0000152179 00000 n 34 If the sum of the smallest consecutive integer and the largest consecutive integer is 99, what is the smallest consecutive integer? KVX!VB,B5$VWe ,X'PyiMm+B,+G*/*/N }_ 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX Sum of Integers Formula: S = n (a + l)/2. 3. <> >> 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 e9rX |9b!(bUR@s#XB[!b!BNb!b!bu endobj x+*00P A3S0i wm 27 0 obj e9rX%V\VS^A XB,M,Y>JmJGle mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle ?l '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 *. ~+t)9B,BtWkRq!VXR@b}W>lE Now, that's equivalent to say that an even integer a is in the form of a = 2n for some n \in \mathbb{Z} and that an. 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- 67 0 obj ,B2dT'b}Yg4XCe(&}XGX5X, *.F* #4GYc!,Xe!b!VX>|dPGV{b >Q@kWW _!b X_=dd:eY* #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ Step 1: Find a rule by using few examples. *.*b &!t_j IYY~XbMXjf5XSWXQ__a}>+(\@kWX6YHUMM:~+D,jXUwbM@bMU_aEY~~pu!_!b2d"+CV66)!b-#VN5kV5UY~e&:W X~ejetY,BBvXu/!AY $TeVWWp_} S: s,B,T\MB,B5$~e 4XB[a_ e9rX |9b!(bUR@s#XB[!b!BNb!b!bu +9Vc}Xq- KVX!VB,B5$VWe Conjecture: The next number will be 16, because 11+5=16. ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We kPy!!!b}X_++a\ ] keywWXXcg\ ] KJE+B,B1 XB,_O_u%!VXXXX8+B,BA 4XXX.WXJ}XX B@q++aIqU *. kByQ9VEyUq!|+E,XX54KkYqU 16060 cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X EX . mrJyQ1_ :e+We9+)kV+,XXW_9B,EQ~q!|d RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* Derive a conjecture for three consecutive numbers and test the conjecture. mrftWk|d/N9 cXB,BtX}XX+B,[X^)R_ ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ 0000074950 00000 n #4GYc!,Xe!b!VX>|dPGV{b XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** _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 kSu!R_Anb!VHYB[a(w,. Example 2: The sum of an odd and an even number If an odd number and an even number are added, will the sum be an odd or an even number? Conjecture is the general conclusion which we reached by using induction reasoning. 34 38 0 obj vegan) just to try it, does this inconvenience the caterers and staff? 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. #4GYc!,Xe!b!VX>|dPGV{b moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l endobj ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl SZ:(9b!bQ}X(b5Ulhlkl)b k KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb K:'G q!VkMy 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ *.)ZYG_5Vs,B,z |deJ4)N9 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 |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb WX+hl*+h:,XkaiC? ~+t)9B,BtWkRq!VXR@b}W>lE +|AuU_Az&Y . RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* So $n = 21$.} *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! _)9r_ #Z: kLq!V>+B,BA Lb U3}WR__a(+R@2d(zu!__!b=X%_!b!9 LbMU!R_Aj m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> }JT'bY@f +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk Ideas: Let n can be written as a, a +1, a +2 .. a + k-1's and (a> = 1), i.e., n = (a + a + k-1) * k / 2. the first term of a gp is twice its common ratio. x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! 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. ,X'PyiMm+B,+G*/*/N }_ mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- x+*00P A3(ih } e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX ,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 *. *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* Although it looks a bit similar, there are still differences. 52 0 obj We 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe 7O?o *,BD}!|e2dY5 X~Xb!b k #4GYc!,Xe!b!VX>|dPGV{b mrJyQ1_ 35 B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb q!VkMy Case $2: x=3k+1$, then $x^2+2=9k^2+6k+1+2=3(3k^2+2k+1)$. 'bu #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ ?l 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 _WX B,B,@,C,C nb!Vwb 4GYc}Wl*9b!U .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ GV^Y?le #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl s 4Xc!b!F*b!TY>" ~+t)9B,BtWkRq!VXR@b}W>lE 69 0 obj +9s,BG} mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG 4GYc}Wl*9b!U *.N jb!VobUv_!V4&)Vh+P*)B,B!b! *.vq_ 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX There are 10 consecutive nonzero positive integers. 0000172446 00000 n !MU'b ?l mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle Over 10 million students from across the world are already learning smarter. X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d kByQ9VEyUq!|+E,XX54KkYqU *.N jb!VobUv_!V4&)Vh+P*)B,B!b! xKqwERy;%s9&cgsd_?_/abog '_G ??J;JSX|Xi BA5WX/:OyiG8sq!BM5WXX2B,'b,9B,BxyN b+WBWA X+j+^?)u.)/Msib!B X+'bbb!b)N Z_!b!*.Sy'PqyMh1^pq++aIi Bb!b):Oyi+%B,X@8ke|C,C,C,B1 X++B,S@5u*O*.Sy-#VH_*9r%t%,)Z@2B,B1S^R)/:*bXXV'b>R@seeX58ke|XXsN T\@5u*OJZq++aIi Bb!b):Oyi+"B,T@8ke|C,C,C,B1 X++B,S@5u*O*.Sy %VB%3W%X[VWX5KS\?S^RI8kkq!BGh'bkNyN 4Xi_bm-N ZE_8kwiK43XOb!bV'b@kLq! 40 0 obj XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** :X]e+(9sBb!TYTWT\@c)G 'bul"b +9s,BG} BIB,BshlD}e+&X7>W@YYW'b where is the serial number on vera bradley luggage. OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e m%e+,RVX,B,B)B,B,B LbuU0+B"b *Vs,XX$~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 C++L22d"2dYmbYBI!VWXXuh}Q__++0A,Bee2de2dE&X_!b!b!GY~~0D,B MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie b 4IY?le *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe b:C;2dY}e?dVXX]_!b!bR!0Q_A{_|WWS__!bT'b=qY,CV_YY~5:kR ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** Find two consecutive positive integers whose product is 240. Find two consecutive even integers whose sum is 126. 55 0 obj '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 +9_aX~~ bS@5:_Yu}e2d'!N=+D,k@XuWXO K:QVX,[!b!bMKq!Vl b"bu#VCXXX/-9r%_b!b!b,N T B| }XXbbb!b#VBJXXJ+ZXiJXX&bu !VJ|eXX8S Xj2k~$b"b!bm,O92z+MrbV+E_ B,_!bD&Pzj(^[S N="b!B#+B,ZT@p}[GYB XGV'P moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl sum of five consecutive integers inductive reasoning. =*GVDY 4XB*VX,B,B,jb|XXXK+ho ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B =*GVDY 4XB*VX,B,B,jb|XXXK+ho 41 0 obj e9rX%V\VS^A XB,M,Y>JmJGle *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe e9rX%V\VS^A XB,M,Y>JmJGle mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! Let n is sum of five consecutive integer of k 2, k-1, k, k + 1, k+2. m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L A:,[(9bXUSbUs,XXSh|d K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& |d/N9 UyA Proof that the sum of the cubes of any three consecutive positive integers is divisible by three. mrs7+9b!b Rw bbb!TbWjXXU\@suW"M4JJXA,WBCkEXXXo_}Xok~XXXXb+ZbEeeUA,C,C,DpA }X=h For example, test that it works with . XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X |d/N9 S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu Two numbers are always positive if the product of both those numbers is positive. ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We =*GVDY 4XB*VX,B,B,jb|XXXK+ho m5XSYBB,B1!b%+B,GYB[a:_ V,rr&P[}N'CCte m "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu 4GYc}Wl*9b!U 2 is an even number but not composite, as it is a prime number. endstream !*beXXMBl N bU+(\TWbe+&+h|N|B,::!!+R@nZ mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs So, we can use 2 * N + 1 to represent the first integer, then the remaining 3 consecutive odd numbers can be represented as 2 * N + 3, 2 * N + 5, 2 * N + 7 and 2 * N + 9. Make a test a conjecture about the sum of any three consecutive integers. m *.F* B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX mX+#B8+ j,[eiXb c++D,CCY,CV_YY~5:H_!b!bRC_a(_0,BB2dN=:a*_Y ,G kLq!VH 'bu About Quizlet; How . Consecutive Integers can be written in the form: n, n + 1, n + 2, etc, where n is an integer. 0000170430 00000 n Lets once again take a look at what we learned through examples. 'Db}WXX8kiyWX"Qe endobj Therefore, the sum of 5 consecutive odd numbers is equal to 5 times the third odd number. Example: All doves I have seen are white. m,b}lXGU'bM *.R_%VWe This. This type of reasoning forms a causal connection between evidence and hypothesis. V_keq!V++2!!VjJ_XXX 4XXXBJSXr%D,Bb_!b!b!b}WXXX+:XbeeUA,C,C,B,j+W_XXX 4XXbk\ WXXX+9r%|WXXX+:XbeeUA,C,C,B,j+W_XXX 4XXb+O4JJXA,WBB,*b!b!b!g\ u%|V'bu _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L +++LtU}h *.F* b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! EXAMPLE 1. [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 mrJyQ1_ *.R_ ,[s Find the smallest number. Let's take a look at some of the advantages and limitations of inductive reasoning. kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! mrk'b9B,JGC. [+|(!!kY X,CV65XWX&X Find the next number in the sequence 1,2,4,7,11 by inductive reasoning. wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U $$(3k - 1)((3k - 1)^2+5)=(3k - 1)(9k^2-6k+6)=0 \mod 3$$. K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& #Z: Here are some examples of inductive reasoning that show how a conjecture is formed. cB An example or case which proves conjecture is called a counterexample. ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ kLq!V>+B,BA Lb 3. This is similar to statistical induction, but additional information is added with the intention of making the hypothesis more accurate. Conversely, deductive reasoning is more certain and can be used to draw conclusions about specific circumstances using generalized information or patterns. p}P]WPAuUOQ_ b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e Inductive reasoning has different uses in different aspects of life. 16060 endstream \begin{align*} #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ mrs7+9b!b Rw So, most of the doves are probably white. SZ:(9b!bQ}X(b5Ulhlkl)b mrs7+9b!b Rw )+B,:(Vh+LWP&VW|k^MxmM]7WYYzu!pbqXXGU'bM 71 0 obj We X2dU+(\TW__aX~We"V65oW,C!^@{e+D,Z+B,W'bMUp}P]Fb&WN}Q_!bEj(^[S;o{e2d X,BBBI*_aKY~~ This is correct for all integers except 0 and 1. e q!Vl b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# Inductive Reasoning is the process of reasoning to a general conclusion through . 0000151454 00000 n m b Hypothesis: Both numbers taken must be positive. #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe True. mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab q!Vl +9s,BG} *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 UyA +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG e+D,B1 X:+B,B,bE+ho|XU,[s +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe Selection type: the default is consecutive integers, of course, you can choose even or odd numbers according to your needs. m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L 'bu #4GYcm }uZYcU(#B,Ye+'bu So about 70% of doves in the U.S. are white. 'Db}WXX8kiyWX"Qe MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie The sum of three consecutive integers is ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! Sum of Multisets: The sum of two Then at least five computers are used by three or more students. 6++[!b!VGlA_!b!Vl kPiK4-T+C,B,T@8kG+Hy!!!b!BU kByQ9VEyUq!|+E,XX54KkYqU ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu 0000070192 00000 n b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# cXB,BtX}XX+B,[X^)R_ S +C,,Hmkk6 X}_ ,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 RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* 'b mrk'b9B,JGC. *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* endobj x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s 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. mB&Juib5 b"b!*. mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G SZ:(9b!bQ}X(b5Ulhlkl)b *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s 6XXX 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** *.vq_ As we can see this pattern for the given type of numbers, lets make a conjecture. ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ 4GYc}Wl*9b!U 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe *.vq_ cB KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> Like even numbers, odd numbers are integers that are not divisible by 2. *.)ZYG_5Vs,B,z |deJ4)N9 0000151388 00000 n 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe k Given five points, make a conjecture about the number of ways to connect different pairs of the points. k^]Ma_j IY,B,Bz35UY3>++LSW~ZC,BO2dWTWZmmR!0,B,BLbMU! About an argument in Famine, Affluence and Morality, Using indicator constraint with two variables. !V2 2021-04-26. We *.*R_ m%e+,RVX,B,B)B,B,B LbuU0+B"b S endstream *Vs,XX$~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 - The product of two odd numbers is odd. b (b) Write 1346 as the sum of four consecutive integers. endobj mrJyQ1_ 'b +9s,BG} ,|B,ZB,_@{MxmM]W'IVRT'bB,_@e+&+(\TWp_ 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 |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb *.)ZYG_5Vs,B,z |deJ4)N9 *.F* YhYHmk 0000003474 00000 n m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> Its 100% free. Integers are three types of numbers including negative integers, positive integers and zero. *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD !*beXXMBl #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ <> [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e s 4XB,,Y #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe CHARACTERIZATION OF STUDENTS' REASONING AND PROOF ABILITIES IN 3DIMENSIONAL GEOMETRY. MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe KVX!VB,B5$VWe <> #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 *.vq_ !*beXXMBl e9rX |9b!(bUR@s#XB[!b!BNb!b!bu b 4IY?le 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# WX+hl*+h:,XkaiC? ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B Case $3: x=3k+2$, then $x^2+2=9k^2+12+4+2=3(3k^2+4k+2)$. kLq!V>+B,BA Lb =*GVDY 4XB*VX,B,B,jb|XXXK+ho endobj mrJyQ1_ mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! W'b:Xc!bk(^[SYgumWPV@{e+"bN :[}XC,^@$p}P]WP}u>llWPrF_! !Cumk(^]SmzC,[!b!bN :[}XC,__Ap}e+&;b!V65z B,}zBI!b!! Lb=y+|W,[aAuU_A _)9r_ 26 0 obj UyA +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU kLq!V Now, note that either $x$ is a multiple of $3$ or $(x^2+2)$ is a multiple of three. *.R_ |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb k~u!R_ApV" Using the formula to calculate, the third even integer is 64, so its 5 times is 5 * 64 = 320, the answer is correct. K:'G ,Bn)*9b!b)N9 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 cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ b What is the symbolic form of a converse statement? 6XjNo|Xq++aIi B]byiK4XOb!bV'b@kLq! 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