Q12 of 110 Page 58

If S1,S2and S3 are the sum of first n, 2n and 3n terms of a geometric series respectively,

then prove that S1(S3 – S2) = (S2 – S1)2.

Sum of n terms =


S1 =


S2 =


S3 =


Putting value of S1, S2 and S3 on the left side, we get:


S1(S3 – S2) =


⇒ S1(S3 – S2) =


⇒ S1(S3 – S2) =


⇒ S1(S3 – S2) =


⇒ S1(S3 – S2) = ………..(1)


Now, we solve the right side by putting S1, S2 and S3 :
(S2– S1)2 =


⇒ (S2– S1)2 = ………….(2)


From (1) and (2), we have:


Left hand side = Right Hand side


Hence Proved.


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