6 The sequence \(\left\{ u _ { n } \right\}\) is such that \(u _ { 1 } = 7 , u _ { 2 } = 37 , u _ { 3 } = 337 , u _ { 4 } = 3337 , \ldots\).
- Write down a first-order recurrence system for \(\left\{ \mathrm { u } _ { \mathrm { n } } \right\}\).
- By solving the recurrence system of part (a), show that \(\mathrm { u } _ { \mathrm { n } } = \frac { 1 } { 3 } \left( 10 ^ { \mathrm { n } } + 11 \right)\).
- Prove that \(\left\{ \mathrm { u } _ { \mathrm { n } } \right\}\) contains infinitely many terms which are multiples of 37 .