114k views
2 votes
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

1 Answer

5 votes

ANSWER

$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

User Mayank Pandya
by
7.4k points