Q11 of 110 Page 58

A geometric series consists of even number of terms. The sum of all terms is 3 times the sum of odd terms. Find the common ratio.

Ans. r = 2

In the G.P.,


Let First term = a,


Common ratio = r


Series: a, ar, ar2,…….arn–1


Sum of all terms =


For odd terms,


a, ar2,………arn–2


First term = a


Common ratio = r2


Number of terms = n/2


Sum of odd terms =


⇒ Sum of odd terms =


Now,


Sum of all terms = 3× Sum of odd terms


⇒ = 3 ×


⇒ (1–r2) = 3(1–r)


⇒ r2–3r + 2 = 0


⇒ r2–2r–r + 2 = 0


⇒ r(r–2)–1(r–2) = 0


⇒ (r–1) (r–2) = 0


r = 1 or r = 2


But r = 1 is not possible, So r = 2.


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