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`        An A.P whose first term is unity and in which the sum of the first half of any even number of terms to that of the second half of the same number of terms is in constant ratio, then find the common difference.`
7 years ago

147 Points
```										Dear Sanchit
let the common difference is d
let 2n number of terms
Sn =n/2 [ 2 + (n-1)d]
and
S2n =2n/2 [ 2+ (2n-1)d]
given
Sn /(S2n -Sn) =  constant
or  (S2n -Sn )/Sn =constant = k
S2n /Sn  -1 =k
or  S2n /Sn = constant =k +1
2n/2 [ 2+ (2n-1)d]  /n/2 [ 2 + (n-1)d]  =k +1
2[ 2+ (2n-1)d]/[ 2 + (n-1)d] = k +1
d= 2(k-1)/{n(3-k) +k -1}
since ratio is independent of n so coefficient of n should be zero
3-k =0
k=3
so d = 2
Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very  quickly. We are all IITians and here to help you in your IIT JEE  & AIEEE preparation. All the best. Regards,Askiitians ExpertsBadiuddin
```
7 years ago
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