Q. 115.0( 1 Vote )

# 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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