Question

Suppose your uncle gives you money during the first 15 days of each month. He gives you $100 onthe first day, $50 the next day, then $25 on the day after that, and follows the same pattern until thefifteenth day. How much would your uncle give you in a year?

Answer 1

Okay, here you have a sequence problem. First, you need to find how much money your uncle gives you each month, and then you multiply that result by 12, which are the months in a year. The first term of the sequence is 100 and each day he gives you half of the previous day. The next formula is the one you need to use:

`\sum ^n_(i\mathop=0)100\cdot(1)/(2^i)=200-100\cdot2^(-n)=200-100\cdot2^(-15)\cong199.997`
`199.997\cdot12=2399.96`