Question 6 - A-Level Maths

6 A sequence is defined by \(a _ { 1 } = 1\) and \(a _ { k + 1 } = 3 \left( a _ { k } + 1 \right)\).

Calculate the value of the third term, \(a _ { 3 }\).
Prove by induction that \(a _ { n } = \frac { 5 \times 3 ^ { n - 1 } - 3 } { 2 }\).