If the sum of an infinite decreasing G.P. is 3 and the sum of the squares of its term is , then write its first term and common difference.

Let the given GP be a,ar,ar²,…

Sum of infinite GP is given by

∴ According to the question

⇒

⇒ a = 3(1-r)

⇒ a =3-3r

⇒ a+3r = 3…(1)

⇒

⇒ the first term is a² and the common ratio is r².

∴ According to the question

⇒

⇒

⇒

⇒

⇒ 2a = 3+3r

⇒ 2a-3r = 3…(2)

Equating 1 and 2 we get

a = 2 and r =1/3