Question

In a G.P. of even number of terms, the sum of all terms is five times the sum of the odd terms. The common ratio of the G.P. is

A. - 4/5

B. 1/5

C. 4

D. none of these

Answer 1

Let,a be the first term and r be the common ratio. The number of terms is 2n.

G.P. ⇒ a, ar, ar², …… (upto 2n terms)

Sum of all terms \(=\frac{a(1-r^{2n})}{1-r}\)

Odd terms G.P. ⇒ a, ar², ar⁴, …… (upto n terms)

Sum of odd terms G.P. \(=\frac{a(1-(r^2)^n)}{1-r^2}\) \(=\frac{a(1-r^{2n})}{1-r^2}\)

Sum of all terms = 5×Sum of odd terms

5(1 – r) = (1 – r²)

r² – 5r + 4 = 0

(r – 1)(r – 4) = 0

r = 1(not possible) and r = 4

So, common ratio of the G.P. = 4