- 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 \(\sum _ { r = 1 } ^ { n } r\) and \(\sum _ { r = 1 } ^ { n } r ^ { 2 }\) to show that for all positive integers \(n\)
$$\sum _ { r = 1 } ^ { n } ( 7 r - 5 ) ^ { 2 } = \frac { n } { 6 } ( 7 n + 1 ) ( A n + B )$$
where \(A\) and \(B\) are integers to be determined.