Question

If the sum of an infinite G.P. be 3 and the sum of the squares of its term is also 3, then its first term and common ratio are (a) 3/2, 1/2 (b) 1/2, 3/2 (c) 1, 1/2 (d) none of these

Answer 1

Given

We take first term= a and common ratio= a

a²+a⁴+a^6+---+-= 3

a+a²+a³+-+-----+- = 3

subtracting

a+a³+a^5+ ----+-- = 0

a= - a³

So answer is non of these (d)