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