Giving recursive definition

Question

I need to give the recursive function of $3n^2$. I'm pretty sure the base case needs to be $3 \cdot 0^2 = 0$, but I don't know where to go from there.

Any help is appreciated.

Answer 1

If $a_n=3n^2$, then $$a_n-a_{n-1}=3n^2-3(n-1)^2=6n-3$$ Therefore, $$a_n=6n-3+a_{n-1}$$ $$a_0=3\cdot 0^2=0$$ is the recursive relation.