Geometric Progression related question.

Question

In a sequence, first term a₁ = 100 and n^th term, a_n = 100 + (a_n-1)/5
If for some integer k, a₅₀ lies between k and (k + 1), then k =

Answer 1

Let's check the first 3 terms:

$a_1 = 100$

$a_2 = 100 + 100/5 = 120$

$a_3 = 100 + 100/5 + 100/25 = 124$

I don't see how this is an arithmetic progression. It's more like a geometric series:

$a_n = \sum_{i=0}^{n-1} 100*(1/5)^i$

This allows a simple geometric series formula. Can you solve it from here?