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

ANSWER

$16,384

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

$r = \frac{2}{1} = \frac{4}{2} = 2$

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