When you were born, both of your rich grandparents made a deal with your parents, to do with what money they'll give you for birthdays. Grandad's deal was :
I'll give you £1 for your first birthday. Then, the amounts that I give you each year will double every time
and Grandma said :
I will start by giving you £1 for your first birthday. Then, the amount I give you will be the combined total of all the last birthday presents that I have ever given you up to that point. Plus, every birthday you have that's a multiple of five, I'll give you an extra five pounds.
a)What amount of money do they each pay you for your 15th birthday
Who would have given you the most after 27 years?
(In reply to re(2): solution
"Plus, you would need to subtract 1 from that 2^13 anyway" is not quite right. Since we are only asking about the amount given ON that birthday, the answer would be 2^13 if the £5 amounts were not involved. Interestingly, the series of amounts starts out 1, 1, 2, 4....that extra 1 at the beginning means that if you were looking for the total given by the 15th year, the answer would be 2^14, not 2^14-1 (still ignoring the £5)
But as you point out, adding those in at £5 and 10 years makes a big difference. The value of £10837 on the 15th birthday is correct, I believe.