- A sequence of terms is defined by
$$u _ { n } = 3 ^ { n } - 2 , \quad n \geq 1 .$$
- Write down the first four terms of the sequence.
The same sequence can also be defined by the recurrence relation
$$u _ { n + 1 } = a u _ { n } + b , \quad n \geq 1 , \quad u _ { 1 } = 1 ,$$
where \(a\) and \(b\) are constants.
- Find the values of \(a\) and \(b\).