The sum s of the first n integers is given by the formula s=1/2n(n+1). how many integers must be taken to have a sum of 325

25

Step-by-step explanation:

We require to solve for n, hence

n(n + 1) = 325

multiply both sides by 2 to eliminate the fraction

n(n + 1) = 650

n² + n = 650

subtract 650 from both sides to have equation in standard form

n² + n - 650 = 0 ← in standard form

(n + 26)(n - 25) = 0 ← in factored form

equate each factor to zero and solve for n

n + 26 = 0 ⇒ n = - 26

n - 25 = 0 ⇒ n = 25

however, n > 0 ⇒ n = 25