anonymous
  • anonymous
The sum of first 14 terms of 1,1.4,1.8,.... is equal to the sum of first n terms of 5.6,5.8,6.0,.... , find the value of n
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
1,1.4,1.8,.... This is in AP with first term 1 and common difference 0.4
anonymous
  • anonymous
Use sum formula of AP
amoodarya
  • amoodarya
14/2(a1+a14)=n/2(5.6+5.6+(n-1)*0.2)

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amoodarya
  • amoodarya
14/2(1+1+13(.4))=n/2(5.6+5.6+(n-1)*0.2)
anonymous
  • anonymous
i did the first A.P and its coming 50.4
anonymous
  • anonymous
S14 =14/2 {2*1 + (14-1)0.4} = 50.4
anonymous
  • anonymous
i am stuck here
anonymous
  • anonymous
5.6,5.8,6.0,.... This is in AP with common difference 0.2 andfirt term 5.6
anonymous
  • anonymous
\[50.4=\frac{ n }{ 2 }[(2*5.6)+(n-1)*0.2]\]
anonymous
  • anonymous
stuck here
anonymous
  • anonymous
Sn=50.4 n/2 { 2*5.6 + (n-1)0.2}=50.4 n{11 - 0.2n}=100.8
anonymous
  • anonymous
2*5.6 its 11.2
anonymous
  • anonymous
11n -0.2n^2 =100.8 11n -2/10 n^2 =100.8 110n -2n^2 =1008
anonymous
  • anonymous
11.2-0.2=11
anonymous
  • anonymous
oh
anonymous
  • anonymous
110n -2n^2 =1008 2n^2-110n+1008=0 n^2-55n+504=0
anonymous
  • anonymous
how did became 110n -2n^2 =1008
anonymous
  • anonymous
|dw:1359028396466:dw|
anonymous
  • anonymous
ok
anonymous
  • anonymous
Now,n^2-55n+504=0 CAN u solve for n
anonymous
  • anonymous
n= -11.61 and n= -43.38
anonymous
  • anonymous
now what?
anonymous
  • anonymous
The Answer should come n=8...i checked the answers
anonymous
  • anonymous
n=8 is surely not the correct solution
anonymous
  • anonymous
the book says that answer is n=8
anonymous
  • anonymous
how will it come 8
anonymous
  • anonymous
Sorry I did a algebra mistake
anonymous
  • anonymous
n=8 is correct
anonymous
  • anonymous
how????? plz plz tell me
anonymous
  • anonymous
Sn=50.4 n/2 { 2*5.6 + (n-1)0.2}=50.4 n/2 {11+0.2n}=50.4 n{11+0.2n}=100.8 11n+0,2n^2=100.8 11n +2/10 n^2 =100.8 110n+2n^2=1008 55n+n^2=504 n^2+55n-504=0 n^2+(63-8)n-504=0 n^2 +63n -8n-504=0 n(n+63)-8(n+63)=0 (n-8)(n+63)=0
anonymous
  • anonymous
Now, either n-8=0 n=8 OR n+63=0 n=-63 BUT n cannot be negative So, n=8
anonymous
  • anonymous
got it?
anonymous
  • anonymous
thanks
anonymous
  • anonymous
welcome

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