Higher November 2017 Paper 6 Q12

(a) A sequence is defined using this term-to-term rule.\[u_{n+1} = \sqrt{2u_n + 15}\]

If \(u_1 = 5\), find \(u_2\). [1]

(b) Another sequence is defined using this term-to-term rule,\[u_{n+1} = ku_n + r\]

where \(k\) and \(r\) are constants.

Given that \(u_2 = 41\), \(u_3 = 206\) and \(u_4 = 1031\), find the value of \(k\) and the value of \(r\). [5]