The ratio of the

The first three terms of a G.P. are:a,ar,ar²

The first six terms of a G.P. are:a,ar,ar²,ar³,ar⁴,ar⁵

It is given that the ratio of the sum of first three terms is to that of first six terms of a GP is 125 : 152.

⇒ a + ar + ar² = 125x & a + ar + ar² + ar³ + ar⁴ + ar⁵ = 152x

⇒ a + ar + ar² + r³( a + ar + ar²) = 152x

⇒ 125x + r³(125x) = 152x

⇒ r³(125x) = 152x - 125x = 27x

⇒

⇒ r = 3/5

Ans:common ratio =