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