2013 YJC P2 Q5

Andy and Bob played a computer game last year.

1. Andy gained \(450\) points on the first day he played. On each subsequent day, he gained \(13\) points less than what he gained on the previous day. He played daily up to and including the day he gained less than \(55\) points. Find the total points Andy gained.
2. Bob gained \(400\) points on the first day he played. On each subsequent day, he gained \(0.9\) times of the points he gained on the previous day. Find the minimum number of days for Bob to gain at least \(95\%\) of the theoretical maximum points he can earn.