_QAXX5l#22!b!b *9B,B,T@seeXU[b)UN,WBW rev2023.3.3.43278. 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 *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD >> 'bul"b a concluding statement reached using inductive reasoning. 'bub!bC,B5T\TWb!Ve [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 ^[aQX e 0000002492 00000 n MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe *.)ZYG_5Vs,B,z |deJ4)N9 let a and b be odd numbers. mrftWk|d/N9 46 0 obj Need to show that UN=2dd_Y,C!J,BB,Z+B,BU:~+Weu5Y@kWW _!b X!%CVVY,C!J,BB%B,B $TeV+h kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! 4 0 obj 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b Determine whether the conjecture is true or false Dividing by 2 always produces a number less than the original number. 7. WX+hl*+h:,XkaiC? b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# 'bul"b #Z: Inductive Reasoning is the process of reasoning to a general conclusion through . q!Vl #4GYc!,Xe!b!VX>|dPGV{b e+D,B,ZX@qb+B,B1 LbuU0R^Ab Learn more about Stack Overflow the company, and our products. Try It! _~WXXX)B,@w #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, endobj cEV'PmM UYJK}uX>|d'b S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu 0000003372 00000 n 2dS_A{Wx}_WWP_!bEhYgY!@Y,CVBY~Xb!b!ez(_|WR__aBY~N=2d3d}W,CeY e"b!VWXXO$! 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? Earn points, unlock badges and level up while studying. The difference between an even integer and an odd integer is odd. Example: All doves I have seen are white. Andy made 4 more stars per minute than Belen. cEZ:Ps,XX$~eb!V{bUR@se+D/M\S cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X p}P]WPAuUOQ_ 0000069875 00000 n cXB,BtX}XX+B,[X^)R_ The conclusions obtained via inductive reasoning are only probable but not certain. 6XjBwj?+WBWA X++b!V)/MsiOyiJK mrJyQ1_ So $n = 21$.} WSB3WXXX+WX+B,C,Cr%$b"b!bm,R_!b!VJSXr%D/ 1. 33 0 obj e9rX |9b!(bUR@s#XB[!b!BNb!b!bu >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ 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 +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe 'Db}WXX8kiyWX"Qe I can prove deductively that they are divisible by $3$ but so far any combination I choose fails to prove the divisibility by $9$. U}[(e+&+h 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe :e+We9+)kV+,XXW_9B,EQ~q!|d 0000176974 00000 n :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e m b k~u!AuU_Ajj,*VX=N :>6'b9d9dEj(^[S n+Vzu!|J #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe That is, the sum of 5 consecutive even numbers is equal to 5 times the third even number. 7|d*iGle e SZ:(9b!bQ}X(b5Ulhlkl)b 0000127093 00000 n b9ER_9'b5 Then state the truth value e WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d mrJyQ1_ KJkeqM=X+[!b!b *N ZY@b!b! .) *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* A number is 20 less than its square. * MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe m 50 0 obj KbRVX,X* VI-)GC,[abHY?le mrJy!VA:9s,BGkC,[gFQ_eU,[BYXXi!b!b!b!b')+m!B'Vh+ sW+hc}Xi s,XX8GJ+#+,[BYBB8,[!b!b!BN#??XB,j,[(9]_})N1: s,Bty!B,W,[aDY X: :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e =*GVDY 4XB*VX,B,B,jb|XXXK+ho KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb *. nb!Vwb About Quizlet; How . mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, ):bKU'bYumkBXO!!k}P]5WcGY~~ U})E}e+e+|>kLMxmMszWUN= ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl endobj Step 3 Test your conjecture using other numbers. 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 Sum of five consecutive numbers equals . !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe mrftWk|d/N9 mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s 6++[!b!VGlA_!b!Vl 34 cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU 2. >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ &= x^3+x^3+3 x^2+3 x+1+x^3+6 x^2+12 x+8\\ Make a test a conjecture about the sum of any three consecutive integers. q!Vl b kLqU RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* GY~MxmM~W,Ce^N=2d"b}XXT'bMUp}P]5W~-e&+h Case $2: x=3k+1$, then $x^2+2=9k^2+6k+1+2=3(3k^2+2k+1)$. SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G cXB,BtX}XX+B,[X^)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: Formula for sum of 'n' terms of an arithmetic sequence: S n = n 2 [ 2 a 1 + ( n - 1) d]. 21 0 obj stream 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. Use inductive reasoning to form a conjecture. 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 endstream 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: sum of five consecutive integers inductive reasoning b endobj Xg&PJ,CV:e&PvE_!b!b!#M`eV+h 0000151995 00000 n +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~~ 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: SR^AsT'b&PyiM]'uWl:XXK;WX:X 6XXX mX8@sB,B,S@)WPiA_!bu'VWe 'bul"b Where does this (supposedly) Gibson quote come from? XbbbUn++W5USbB,B,*.OB!lb)UN,WBW endstream The case which shows the conjecture is false is called a counterexample for that conjecture. *.R_ 364 0 obj <>stream *.*R_ cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ wV__a(>R[S3}e2dN=2d" XGvW'bM :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! S"b!b A)9:(OR_ 'bu bbb!b!VHJXX:B,SXr%D,L4g\ WXXX+:UNk:*eeX5Xi5%+!b!b!C,C/+-"BI,WBW K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe ,[s ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ <> *.)ZYG_5Vs,B,z |deJ4)N9 wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U >X@{MxmM]W'|bWse+(VXX[V_!b!b!Te [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s q++aIi @*b!VBN!b/MsiR"2B,BA X+WXhg_"b!*.SyR_bm-R_!b/N b!:Oyq,U++C,B,T@}XkLq2++!b!b,O:'Pqy5 cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s +9s,BG} +MrbVkB,B_fiGkeq!V+(F,C,C moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X kLqU 'bub!bC,B5T\TWb!Ve nb!Vwb +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe Notice that the sum of the five . G. sum of five consecutive integers inductive reasoning 2022. . #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 'b Let us consider two integer numbers say -2 and -3. endstream U}S*+ Ne^@2dY]S9_=BYu!U}WW _; Choose the correct conjecture for the following? Truth value: False, 0 Step 1 1 of 3. mrJyQ1_ How to Sum Integers 1 to n. You dont need to be a math whiz to be a good programmer, but there are a handful of equations you will want to add to your problem solving toolbox. e9rX%V\VS^A XB,M,Y>JmJGle We _)9r_ mX8@sB,B,S@)WPiA_!bu'VWe k 47 0 obj |d/N9 B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX stream mrk'b9B,JGC. S"b!b A)9:(OR_ S 9b!b=X'b 0000008844 00000 n :e+We9+)kV+,XXW_9B,EQ~q!|d 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe 'bub!bC,B5T\TWb!Ve _)9r_ #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ #4GYc!,Xe!b!VX>|dPGV{b 'b This reasoning gives a chance to explore the hypothesis in a wider field. 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 Where possible, show work to support your conclusion. ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ Use inductive reasoning to show that the sum of five consecutive integers . !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe *.R_ 0000152370 00000 n *.)ZYG_5Vs,B,z |deJ4)N9 $VRr%t% +Wb(jb!bC@}e*12B,B,Zv_!b!VJ,CjPUiJK&kc}XXz+MrbV+b5 K:'G 0000004910 00000 n *. mB&Juib5 *.*b 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe mrk'b9B,JGC. Set individual study goals and earn points reaching them. mX+#B8+ j,[eiXb 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! knXX5L b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! 9b!b=X'b C++L22d"2dYmbYBI!VWXXuh}Q__++0A,Bee2de2dE&X_!b!b!GY~~0D,B kaqXb!b!BN 'bu (o%D(_Ok1pLukLy'V$W#sp4UX 49 I~&cM%]J]u_132>IM}`fZ;C{2bu^e{oTrwl%E(yciJ#g'Wbh^?Uw)+ROQ_H],3^Q =4__f%Wm#$SrNJQ0J\G3st5ZFKG(-=Ig'Zr'UjZM,?I>`< ;SlvQ|f4v!@&V=7]lLc@17p$I8'8}O~d`Yeup$@bh ; P.#ra(F$xlG&g@rRb (E#Q ] t@)$gx}G:R )_a:kY5!V@e+L(++B,7XS5s*,BD}VE}WN5+D,C!kxuY}e&&e As far as I can see. m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> mrs7+9b!b Rw Generally, we subconsciously make decisions based on our past observations and experiences. *. #T\TWT\@W' Sign up to highlight and take notes. >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ ,X'PyiMm+B,+G*/*/N }_ To make a conjecture, we first find a pattern. mX+#B8+ j,[eiXb S 2021-04-26. 0000155651 00000 n *.vq_ OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e + 0000094672 00000 n cB ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B But true observations by deductive reasoning will lead to true conjecture. mrftWk|d/N9 two separate circles that show that the two items have no relation, phil 305 midterm: kant, utilitarian, locke, s. UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV Make a conjecture about a given pattern and find the next one in the sequence. mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe Number 20 ends with 0. e+D,B,ZX@qb+B,B1 LbuU0R^Ab +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU How to Sum Integers 1 to n. You dont need to be a math whiz to be a good programmer, but there are a handful of equations you will want to add to your problem solving toolbox. e _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L m% XB,:+[!b!VG}[ e9rX |9b!(bUR@s#XB[!b!BNb!b!bu *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* 0dfjWP(0Q_Az&Y!:_Yu!!MxmM]W'bMB,B,R@$AuL_ We cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ 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. mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! #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 KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb KVX!VB,B5$VWe moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l Disconnect between goals and daily tasksIs it me, or the industry? 60 0 obj e+D,B1 X:+B,B,bE+ho|XU,[s Stop procrastinating with our study reminders. 7|d*iGle ?l m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G ~+t)9B,BtWkRq!VXR@b}W>lE *.N jb!VobUv_!V4&)Vh+P*)B,B!b! endobj *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD SZ:(9b!bQ}X(b5Ulhlkl)b Given a number N, write a function to express N as sum of two or more consecutive positive numbers. kSu!R_Anb!VHYB[a(w,. kLq!VH *. j XYYuu!b}lXB,BCe_!b=XSe+WP>+(\_A*_ B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb &= 3\left ( x^{3}+3x^{2}+5x+3 \right )\\ XA 2, 2 XB} 1 2}, 2 XC 3, 10 XD 2, 21 23. For consecutive even or odd 278+ Experts 9.1/10 Star Rating 55343+ Delivered Orders Get Homework Help X+WBW Be perfectly prepared on time with an individual plan. :X]e+(9sBb!TYTWT\@c)G cEZ:Ps,XX$~eb!V{bUR@se+D/M\S BNxmMY *. 67 0 obj Does ZnSO4 + H2 at high pressure reverses to Zn + H2SO4? +++L'bi&WV@fj*Y2d^@{WXU&O~OXX[hY~ *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD ^[aQX e :XIWSXWXE22 !!b!_vB,B,*.O90 endstream by Sum of Consecutive Integers Word Problems. endstream +9Vc}Xq- KbRVX,X* VI-)GC,[abHY?le 0000056514 00000 n B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ <> ~iJ;WXX2B,BA X}+B,J'bbb!bUSbFJXXsNAub!b)9r%t%,)j? The use process is also very simple, input the first integer, then select the integer type. ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ mB#V_!W'bZ_Ap7|b cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X b 4IY?le This is similar to statistical induction, but additional information is added with the intention of making the hypothesis more accurate. Prime numbers only have two factors, 1 and itself, If prime numbers only have 2 factors, then they are 1 and itself. kaqXb!b!BN A:,[(9bXUSbUs,XXSh|d This type of reasoning forms a causal connection between evidence and hypothesis. kmR!e:fjk*,B,AA!b=XS5s+(\_A{WU'b&WXuC,CC!UW!0,B,zbI9d=+|W~~1e&XHu!!u_YY~ e!b!|XXLbMU!p}Q_++)0,2dEhYe2de+L(rzWXXe+LWe+B 0000095472 00000 n _WX B,B,22 !!b!b-6'bbb &VWmT9\ ] +JXXsZ+B,jbg\ ] KZ+B,jb!b!bmUbbbUWXXh+JSXr%D,B9-b!b53W%b!b5**eeXX+B,B 4XXXb)UN,WBW endobj endstream *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb kLq!VH K:'G #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! #4GYc!,Xe!b!VX>|dPGV{b moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l Deductive reasoning is a reasoning method that makes conclusions based on multiple logical premises which are known to be true. *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b |d/N9 K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU b9ER_9'b5 Example #4: Look at the following patterns: 3 -4 = -12 The sum of 5 consecu 1. Number expressed as sum of five consecutive integers *.F* ^[aQX e 0000053628 00000 n Difference between consecutive perfect squares 22- 42= 4 - 16 = 2 The difference between consecutive perfect squares is odd. mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU *.vq_ For example: What is the sum of 5 consecutive odd numbers 81, 83, 85, 87 and 89? #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl m% XB,:+[!b!VG}[ +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk _)9r_ #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ B,B:Y~ b&uF_}AuU_ABAYe2d%| )C $Pe!b!V;* What is the symbolic form of and inverse statement? 43 0 obj 58 0 obj wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U +9s,BG} m%e+,RVX,B,B)B,B,B LbuU0+B"b mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs True/False: What is the answer to the conjecture? +9s,BG} x+*00P A3S0i wd EX . KVX!VB,B5$VWe UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe #Z: b"b!VW?s|J8J8WXXX+:XB*eeXXM|J8kW5XiJXXO&K|XXX+WWq2B,B,ZY@z+E,C,C +9Vc}Xq- *.*b Example: I have seen white doves in the park. XXXKXXXX m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L 0000004933 00000 n ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We endobj 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). +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e B,B, *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD In inductive reasoning, true observations might have false conjecture. Complete the conjecture: The square of any negative number is ? The sum of 5 consecutive integers can be 100. XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe mX+#B8+ j,[eiXb endobj 42 0 obj mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe _,9rkLib!V |d*)M.N B}W:XXKu_!b!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 B,Bs&eWP>+ +9Vc}Xq- +^u!_!b2d"+CV66)!bNkB5UY~e&:W~ZC,B2de2dE:WZmmRC_!b!V;:Xu_!b!k UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV cEV'PmM UYJK}uX>|d'b *.R_%VWe KJkeqM=X+[!b!b *N ZY@b!b! 10 0 obj $$(3k - 1)((3k - 1)^2+5)=(3k - 1)(9k^2-6k+6)=0 \mod 3$$. 9b!b=X'b mrs7+9b!b Rw :X\ :XXab]b!V*eeXU=_vB,B,*.O9Z>+BJSXr%D, #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ K:QVX,[!b!bMKq!Vl *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* Conjecture: The next number will be 16, because 11+5=16. mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs log(x+2)log(x1)=log(x+2)log(x1)\frac { \log ( x + 2 ) } { \log ( x - 1 ) } = \log ( x + 2 ) - \log ( x - 1 ) K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& 14 0 obj The difference between two numbers is always less than its sum. kLq!V <> +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX |d/N9 Make and test conjecture for the sum of two even numbers. Top Questions. q++aIi *|eeU+C,B,zb!b!Vqy!!!}_!+a\ ] +JXXS|XXX+g\ ] K|eXX8SbbUWXXH_5%V/,B,BC,C,CB,W"bV The sum of 5 consecutive integers can be 100. b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# 6XXX m%e+,RVX,B,B)B,B,B LbuU0+B"b Inductive reasoning is not logically valid. KbRVX,X* VI-)GC,[abHY?le . #4GYc!,Xe!b!VX>|dPGV{b X2dU+(\TWu__aX~We"V65u;}e2d X,BB+B,W'bMUp}P]RW~~!bS_A{WX9C[2dYC,C_!b!_!b!V:kRJ}++ U'bY@uduS-b!b p}P]WPAuU_A/GYoc!bS@r+rr^@Mxu![ XB,BCS_Ap}:%VK=#5ufmM=WYb9d b9ER_9'b5 0000094336 00000 n So if any one of the cases is false, the conjecture is considered false. 4GYc}Wl*9b!U >S?s|JJXR?B,B,B,W?)u.*kaq! ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu 6++[!b!VGlA_!b!Vl Uu!:vC,C!+R@z&PC__!b!b-N :AuU_DQ_=++LWP>$QCC,C!+R@z&P&U'bZ_AYoWe&+(\TW XGk;}XoU'bYC65u^_!b!b-N :AuU_JQ_=++LWP>>[[SYo GV^Y?le x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! UyA kLq!V x 1 (x 1 1) 1 (x 1 2) 1 (x 1 3) 1 (x 1 4) 5 __?__ 22. b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B ,Bn)*9b!b)N9 This formula can also be understood as that the sum of 5 consecutive integers is equal to 5 times the third integer. mrJyQ1_ The sum of five consecutive integers is divisible by 5 is indeed true; for if we denote the five consecutive integers by n, then n . stream b9ER_9'b5 x+*00P A3S0ih ~* 68 0 obj |d/N9 e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e mrk'b9B,JGC. #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl endobj 'bub!bC,B5T\TWb!Ve UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu endobj KVX!VB,B5$VWe 8 0 obj s 4Xc!b!F*b!TY>" K:QVX,[!b!bMKq!Vl endobj So, we can use 2 * N + 1 to represent the first integer, then the remaining 3 consecutive odd numbers can be represented as 2 * N + 3, 2 * N + 5, 2 * N + 7 and 2 * N + 9. +9_aX~~ bS@5:_Yu}e2d'!N=+D,k@XuWXO KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! K:'G OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e 34 e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX !*beXXMBl <> +9s,BG} wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U m% XB,:+[!b!VG}[ *Vs,XX$~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 q!VkMy kLq!V K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s KVX!VB,B5$VWe #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ The smaller of two consecutive integers is eight less than A straightforward word problem solved using an equation. |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s SR^AsT'b&PyiM]'uWl:XXK;WX:X R22 !!b!b5+/,B,BC,CC ,X'PyiMm+B,+G*/*/N }_ Step 3: Test the conjecture for a particular set. b"b! %PDF-1.7 % s 4Xc!b!F*b!TY>" EXAMPLE 1 Make a Conjecture Complete the conjecture. mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl b 44 0 obj 1 1. sum of five consecutive integers inductive reasoning

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