Question

Find the reason for the geometric progression in which a1 = 1, n = 3, S3 = 157

Answer 1

S3 = 1(1-r^3)/(1-r) = 157

1+r+r^2 = 157
r^2+r-156 = 0
(r-12)(r+13) = 0
r = 12 or -13
So, the GPs are

1,12,144,...
1,-13,169,...