- (a) Use the standard results for summations to show that for all positive integers \(n\)
$$\sum _ { r = 1 } ^ { n } ( 5 r - 2 ) ^ { 2 } = \frac { 1 } { 6 } n \left( a n ^ { 2 } + b n + c \right)$$
where \(a\), \(b\) and \(c\) are integers to be determined.
(b) Hence determine the value of \(k\) for which
$$\sum _ { r = 1 } ^ { k } ( 5 r - 2 ) ^ { 2 } = 94 k ^ { 2 }$$