T.Madas - Recurrence Relations Question 41

A sequence of numbers is defined by the recurrence relation for \(n\ge 1\)

\({{u}_{n+1}}=k{{u}_{n}}+6\quad {{u}_{1}}=4\),

where \(k\) is a non zero constant.

1. Find, in terms of \(k\), the value of \({{u}_{2}}\) and the value of \({{u}_{3}}\).
2. Given that \({{u}_{3}}=10\) find the possible values of \(k\).

The sequence tends to a limit \(L\).

3. Find the value of \({{u}_{4}}\).
4. Determine the value of \(L\).