Question 6 - A-Level Maths

6 A sequence is defined by \(a _ { 1 } = 7\) and \(a _ { k + 1 } = 7 a _ { k } - 3\).

Calculate the value of the third term, \(a _ { 3 }\).
Prove by induction that \(a _ { n } = \frac { \left( 13 \times 7 ^ { n - 1 } \right) + 1 } { 2 }\).