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

Desmond’s monthly savings form an arithmetic sequence: he saves $25 in the first month and $5 more each month. After 30 months, his total is 30/2 × [2(25) + 29(5)] = $2,925, which is not enough. After 31 months, his total is 31/2 × [2(25) + 30(5)] = $3,100, so he first has enough after 31 months, choice A.

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