The sum to infinity of a GP is 27 and sum of squares of the terms is 243 , Find the common ratio
a)1/2 b)2 c)3 d)1/3 e) 1
a)1/2 b)2 c)3 d)1/3 e) 1
OA: A
point 1: a + ar + ar^2.........infinity = a/ (1-r) = 27 -----(1)
point 2: a^2 + a^2 r^2......infinity = a^2/(1-r^2) = 243
point 2 can be written as a/(1-r) * a/(1+r) = 243
27 * a/(1+r) = 243
so, a/(1+r) = 9 ------(2)
divide (1) by (2)
(1+r)/(1-r) = 3
on solving this you will get r = 1/2 = common ratio
1+r = 3-3r
4r = 2
r = 1/2
