Answer:
It will take 5 months to save the money to buy a video game system
Step-by-step explanation:
Tammi is planing to buy a video game system for $310. Each month she doubles the amount she saves the previous month. This means that the amount that she has for each month is increasing in geometric progression. The formula for the sum of n terms of a geometric sequence is expressed as
Sn = a(r^n - 1)/r - 1)
Where
r is the common ratio
a is the first term
n is the number of terms
From the information given,
a = $10
r = 2
Sn = 310 (cost of the video game system)
n is the number of years. Therefore
310 = 10(2^n - 1)/(2 - 1)
31 = 2^n - 1
2^n = 32
2^n = 2^5
n = 5
