4. A sequence \(\left\{ u _ { n } \right\}\), where \(n \geqslant 0\), satisfies the recurrence relation
$$u _ { n + 1 } + 3 u _ { n } = n + k$$
where \(k\) is a non-zero constant.
Given that \(u _ { 0 } = 1\)
- solve the recurrence relation, giving \(u _ { n }\) in terms of \(k\) and \(n\).
Given that \(u _ { n }\) is a linear function of \(n\),
- use your answer to part (a) to find the value of \(u _ { 100 }\)
TOTAL FOR DECISION MATHEMATICS 2 IS 40 MARKS
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