Question

If you get a penny a day from your uncle and each day he doubles the amount he gave you on the previous day how much would he give you on the twentieth day

Answer 1

Answer: On the 20th day, he will give $5242.88

Explanation: This is a geometric series with elements:

initial value (
`a_(0)`) = 0.01

ratio = 2

At the twentieth day means the 20th term, i.e. n = 20.

To determine that term, use the formula:
`a_(n) = a_(0).r^(n-1)`

Substituing terms:

`a_(20) = 0.01.2^(20-1)`

`a_(20) = 0.01.2^(19)`

`a_(20) = 0.01.524288`

`a_(20) = 5242.88`

Then, on the 20th day, your uncle gave to you $5242.88