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\frac{1}{2^i}=200-100\cdot2^{-n}=200-100\cdot2^{-15}\cong199.997$$199.997\cdot12=2399.96$