From (2):
Now substitute 2a with d in (1).
Spoiler:
The sum of the first 100 terms of an arithmetic progression is 5000, the first, second and fifth of this progression are three consectuive terms of a geometric progression. Find the value of the first term, and the non-zero common difference of the arithmetic progression.
I only manage to get
(100/2) (2a + 99d) = 5000----(1)
(a+d)^2 = a(a + 4d) ----(2)
I try to substitute, but I just can't get the answer. Am I moving in the wrong direction?