Solve the recurrence relation $a_n =1.04*a_{n−1}+100, a_0 =0$

Question

How do I do this? We're currently learning how to solve nonhomogeneous recurrence relations.

Answer 1

Hint:

1. Shift the term with $a_{n - 1}$ to the left.
2. Divide throughout by $1.04^n$.
3. Do a summation on both sides.
4. LHS telescopes and almost everything is cancelled out.
5. RHS is just a geometric series.