The sum of the first 100 terms of an arithmetic progression is 10000; the first, second and fifth terms of this progression are three consecutive terms of a geometric progression. Find the first term a and the non-zero common difference, d, of the arithmetic progression. (Answer: a = 1, d = 2)

I found:

2a + 99d = 200

After which, I'm stuck.

Thanks in advance if you could help with this question!