Problem

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

Use the standard results for $\displaystyle\sum_{r=1}^{n} r$ and $\displaystyle\sum_{r=1}^{n} r^2$ to show that for all positive integers $n$

$\sum_{r=1}^{n} (7r + 5) = \frac{6n(7n + 11)}{2}$

where $A$ and $B$ are integers to be determined.