Question

a1 = 1, an = an-1 + 2n + 3, n≥2
Find the closed formula

Answer 1

Your sequence is this;
1, 8, 16, 26, 39, 56, 78, 106, ...

Which is equivalent to this:
1 = 7n+1
8 = 7n+1
16= 7n+2
26= 7n+5
39= 7n+11
56= 7n+21
78= 7n+36
106=7n+57

1,1,2,5,11,21,36,57, ...
This page describes how to generate the sequence: http://oeis.org/A050407





If you're doing this as part of a course, you may be expected to use a more specific method of solving the recurrence.

You should probably specify the method you're supposed to be using so we can help you understand it.