Mathematics

An arithmetic progression grows predictably, and its sum formula $S_n = \frac{n}{2}(2a + (n-1)d)$ lets you find how many terms you need without listing them all. The key is setting up an inequality—you want the smallest $n$ where the sum exceeds 260—then solve for $n$ by rearranging the formula into a quadratic. Since $n$ must be a whole number, round up to find the answer.

An arithmetic progression grows predictably, and its sum formula $S_n = \frac{n}{2}(2a + (n-1)d)$ lets you find how many terms you need without listing them all. The key is setting up an inequality—you want the smallest $n$ where the sum exceeds 260—then solve for $n$ by rearranging the formula into a quadratic. Since $n$ must be a whole number, round up to find the answer.