Question

Nadir saves $1 the first day of a month, $2 the second day, $4 the third day, and so on. He continues to double his savings each day. Find the amount that he will save on the fifteenth day.

$16,384
$29
$32,768
$8192

Answer 1

$16,384

Step-by-step explanation

From the question we have that,

Nadir saves $1 the first day of a month, $2 the second day, $4 the third day, and so on.

This forms a geometric sequence,

`1,2,4,...`

The first term of this sequence is

`a = 1`

The common ratio is

`r = (2)/(1) = (4)/(2) = 2`

The general term of a geometric sequence is given by the formula:

`f(n) = a {r}^(n - 1)`

To find the 15th term, we plug in a=1, r=2 and n=15.

`f(15) = 1 {(2)}^(15 - 1)`

`f(15) = {2}^(14)`

`f(15) = 16384`

The amount he will save on the 15th day is $16,384