- A sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by
$$\begin{aligned}
u _ { n + 1 } & = b - a u _ { n }
u _ { 1 } & = 3
\end{aligned}$$
where \(a\) and \(b\) are constants.
- Find, in terms of \(a\) and \(b\),
- \(u _ { 2 }\)
- \(u _ { 3 }\)
Given
- \(\sum _ { n = 1 } ^ { 3 } u _ { n } = 153\)
- \(b = a + 9\)
- show that
$$a ^ { 2 } - 5 a - 66 = 0$$- Hence find the larger possible value of \(u _ { 2 }\)