- A sequence of terms \(\left\{ t _ { n } \right\}\) is defined for \(n \geq 1\) by the recurrence relation
$$t _ { n + 1 } = k t _ { n } - 7 , \quad t _ { 1 } = 3$$
where \(k\) is a constant.
- Find expressions for \(t _ { 2 }\) and \(t _ { 3 }\) in terms of \(k\).
Given that \(t _ { 3 } = 13\),
- find the possible values of \(k\).