- (a) An arithmetic series has a common difference of 7 .
Given that the sum of the first 20 terms of the series is 530 , find
- the first term of the series,
- the smallest positive term of the series.
(b) The terms of a sequence are given by
$$u _ { n } = ( n + k ) ^ { 2 } , \quad n \geq 1$$
where \(k\) is a positive constant.
Given that \(u _ { 2 } = 2 u _ { 1 }\), - find the value of \(k\),
- show that \(u _ { 3 } = 11 + 6 \sqrt { 2 }\).