Question 7 - A-Level Maths

7 It is given that \(u _ { n } = 13 ^ { n } + 6 ^ { n - 1 }\), where \(n\) is a positive integer.

Show that \(u _ { n } + u _ { n + 1 } = 14 \times 13 ^ { n } + 7 \times 6 ^ { n - 1 }\).
Prove by induction that \(u _ { n }\) is a multiple of 7 .