Guest

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.

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.

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

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 Experts
Badiuddin

Think You Can Provide A Better Answer ?

ASK QUESTION

Get your questions answered by the expert for free