9. A cyclist aims to travel a total of 1200 km over a number of days.
He cycles 12 km on day 1
He increases the distance that he cycles each day by \(6 \%\) of the distance cycled on the previous day, until he reaches the total of 1200 km .
- Show that on day 8 he cycles approximately 18 km .
He reaches his total of 1200 km on day \(N\), where \(N\) is a positive integer.
- Find the value of \(N\).
The cyclist stops when he reaches 1200 km .
- Find the distance that he cycles on day \(N\). Give your answer to the nearest km .