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

If price of laptop=x
Let number of months required to save the necessary amount be y
5*2^y=x
2^y=x/5
y=log2 x/5

Answer 2

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.

$\frac{10}{5}=2$

$\frac{20}{10}=2$

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.

$Sn= \frac{a(1-r^{n}) }{1-r}$

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.

$S_6=\frac{5(1-2^{6}) }{1-2}$

$=\frac{5(1-64)}{-1}$

$=315$

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