5 Two heavyweight boxers decide that they would be more successful if they competed in a lower weight class. For each boxer this would require a total weight loss of 13 kg . At the end of week 1 they have each recorded a weight loss of 1 kg and they both find that in each of the following weeks their weight loss is slightly less than the week before. Boxer A's weight loss in week 2 is 0.98 kg . It is given that his weekly weight loss follows an arithmetic progression.

1. Write down an expression for his total weight loss after \(x\) weeks.
2. He reaches his 13 kg target during week \(n\). Use your answer to part (i) to find the value of \(n\).
   Boxer B's weight loss in week 2 is 0.92 kg and it is given that his weekly weight loss follows a geometric progression.
3. Calculate his total weight loss after 20 weeks and show that he can never reach his target.