10 The sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by \(u _ { n } = 5 ^ { n } + 2 ^ { n - 1 }\).
- Find \(u _ { 1 } , u _ { 2 }\) and \(u _ { 3 }\).
- Hence suggest a positive integer, other than 1 , which divides exactly into every term of the sequence.
- By considering \(u _ { n + 1 } + u _ { n }\), prove by induction that your suggestion in part (ii) is correct.
\section*{OCR}