Formula for a sequence

I have this sequence:
$-2, 1, 6, 13, 22, 33, ...$

where each term is the previous plus an odd number. The odd numbers are increasing from 3. I am asked to find an explicit formula with respect to $n$ which can give me the $n$-th number in the sequence. The sequence starts at $n = 1$.

I tried to find a pattern, without success. I then tried to write the sequence as a recursive formula:
$a_1 = -2$
$a_{n + 1} = a_n + 2n + 1$

and then I got stuck.

Can you please advice me about the way to go?

Thanks,
rubik

Answer

Hint: Add $3$ to every number in your sequence.

Remark: A related result is that the sum of the first $n$ odd positive integers is equal to $n^2$. This follows easily from the fact that $n^2-(n-1)^2=2n-1$. There is also an attractive proof without words.