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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.

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reinaester523

Answer:

$315

Step-by-step explanation:

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

[tex]\frac{10}{5}=2[/tex]

[tex]\frac{20}{10}=2[/tex]

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.

[tex]Sn= \frac{a(1-r^{n}) }{1-r}[/tex]

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.

[tex]S_6=\frac{5(1-2^{6}) }{1-2}[/tex]

[tex]=\frac{5(1-64)}{-1}[/tex]

[tex]=315[/tex]

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