What is the sum of the odd integers from 11 through 39, inclusive?
I know that the sum of an arithmetic series, which is a sequence of numbers with a constant difference between consecutive terms, is given by the formula S_n = n/2 (a_1 + a_n), where n is the number of terms, a_1 is the first term, and a_n is the last term. In this case, the odd integers from 11 through 39 form an arithmetic series with a common difference of 2. To find n, I can use the formula a_n = a_1 + (n-1)d, where d is the common difference. Substituting the given values, I get 39 = 11 + (n-1)2. Solving for n, I get n = 15. So there are 15 odd integers in the series. Now I can plug in n, a_1, and a_n into the formula for the sum. I get S_15 = 15/2 (11 + 39). Simplifying, I get S_15 = 375. 