# Recurrences seem lovely!

**Discrete Mathematics**Level 4

A sequence starts with \(a_0=0\) and the next term is \(a_1=1\).

If the further terms are given by

\(\displaystyle a_n= 7a_{n-1}- 10a_{n-2} + 7\)

Then find the last 3 digits of \(a_{20}\).

**Details** :- If you don't know how to get the solutions for recurrence relations, you may try to learn it here.

This note will prove helpful in the coming problems of this series.

First Problem is bit easier than this one.