Question

In January, Desmond begins saving $25 per month for a used car. Each month, he is able to save $5 more than the previous month. After how many months will Desmond first have enough money to purchase a $3,000 used car?

Answer 1

31 months i think. (2 years and 7 months.)

Answer 2

Answer: After 31 months, Desmond first have enough money to purchase a used car.

Explanation:

Since we have given that

Saving per month for a used car = $25

Each month he is able to save = $5 more than the previous month

If we have $3000 to purchase a used car.

So, we need to find the number of months Desmond to have enough money.

Our sequence will be

25,30,35,..............3000

So, it becomes,

`S_n=(n)/(2)(2a+(n-1)d)\\\\3000=(n)/(2)(2* 25+(n-1)5)\\\\6000=n(50+5n-5)\\\\6000=n(45+5n)\\\\6000=45n+5n^2\\\\1200=9n+n^2\\\\n^2+9n-1200=0\\\\\text{ by solving by quadratic formula, we get that}\\\\n\approx 31,-43`

Months can't be negative, So,

n = 31 months.

Hence, After 31 months, Desmond first have enough money to purchase a used car.