8 P74086A   7. Martina decides to open a bank account to help her to save for a holiday. Each month she puts £k into the account and allows herself to spend one quarter of what was in the account at the end of the previous month. Let un (where n 1) represent the amount in the account at the end of month n. Martina has £k in the account at the end of the first month. (a) By setting up a first order recurrence relation for un+1 in terms of un, determine an expression for un in terms of n and k. (6) At the end of the 8th month, Martina needs to have at least £1750 in the account to pay for her holiday. (b) Determine, to the nearest penny, the minimum amount of money that Martina should put into the account each month. (2) (Total for Question 7 is 8 marks)