APPLIED-COURSE-mocktest-2

Question

for whole number n, consider the following recurrence relation defined as

$a_{n+2}=(n+3)a_{n+1}-(n+2)a_n$

and $a_1=1,a_2=3$

find $( \sum_{k=1}^{2015}a_k)(mod\; 100)$ is _

Comments

I got the sum as $1 + 2016 \times a_{2014}$, but don't know how to find the value of $a_{2014}$.

Any ideas?