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?

Desmond’s monthly savings form an arithmetic sequence: $25, $30, $35, and so on. After 30 months, he will have saved 30 × ($25 + $170) ÷ 2 = $2,925, which is not enough. After 31 months, he will have saved 31 × ($25 + $175) ÷ 2 = $3,100, so the first month he can afford the car is 31 months.

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