# How do we find the $n+2$th term of the series $1 + (3+5) + (7+9+11)+\dots$?

We have the series $1 + (3+5) + (7+9+11)+\dots$.

We need to find the $n+2$th term and hence summation of the series up to this term.

However hard we try we do not seem to be able to fit this series to a pattern.

$$a_{1}=1=1^3\\a_{2}=3+5=8=2^3\\a_{3}=7+9+11=27=3^3\\a_{4}=13+15+17+19=64=4^3\\...\\a_{n}=n^3\\so\\a_{n+2}=(n+2)^3$$