Question

Stella wants to save money to buy a new laptop. Every month she sets aside an increasing amount of money to save for the laptop. In her first month, Stella has $5 saved. In the second month, she has $10, and in the third month, she has $20 set aside for the laptop.

Answer 1

$315

Explanation:

First, determine if this situation represents a geometric series by finding the common ratio between successive terms as shown below.

`(10)/(5)=2`

`(20)/(10)=2`

Stella's amount of money saved for the laptop is a finite geometric series. Use the formula below to find the sum of the first n terms in the sequence, where a is the first term and r is the common ratio between successive terms.

`Sn= (a(1-r^(n)) )/(1-r)`

Find the sum of the terms in the sequence by using the formula for the sum of a finite geometric series. The first term of the sequence is 5, so a = 5. The common ratio is 2, so r = 2. To find the amount of money Stella has after 6 months, set n equal to 6.

`S_6=(5(1-2^(6)) )/(1-2)`

`=(5(1-64))/(-1)`

`=315`

So, after 6 months, Stella will have $315.