Sequence and Series - Problems involving inequalities

Ashley and Billie are swimmers training for a competition.

1. Ashley trains for \(12\) hours in the first week. She decides to increase the amount of time she spends training by \(2\) hours each week. Find the total number of hours she spends training during the first \(15\) weeks.[3]
2. Billie also trains for \(12\) hours in the first week. She decides to train for \(10 \%\) longer each week than the previous week.[4]
   1. Show that in the third week she trains for \(14.52\) hours.
   2. Find the total number of hours she spends training during the first \(15\) weeks.
3. In which week will the time Billie spends training first exceed \(50\) hours?[4]