Tammi is planing to buy a video game system for $310. Each month she doubles the amount she saves the previous month. If she saves $10 the first month, in how many months will Tammi have enough money to buy the video game system?

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