Answer: After 31 months, Desmond first have enough money to purchase a used car.
Step-by-step 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,
[tex]S_n=\frac{n}{2}(2a+(n-1)d)\\\\3000=\frac{n}{2}(2\times 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[/tex]
Months can't be negative, So,
n = 31 months.
Hence, After 31 months, Desmond first have enough money to purchase a used car.
