11.
A sequence is defined by
$$\begin{aligned}
u _ { 1 } & = 600
u _ { n + 1 } & = p u _ { n } + q
\end{aligned}$$
where \(p\) and \(q\) are constants.
It is given that \(u _ { 2 } = 500\) and \(u _ { 4 } = 356\)
- Find the two possible values of \(u _ { 3 }\)
- When \(u _ { n }\) is a decreasing sequence, the limit of \(u _ { n }\) as \(n\) tends to infinity is \(L\). Write down an equation for \(L\) and hence find the value of \(L\).
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