What is the sum of the first (15) terms of the arithmetic progression (-5,-1,3,\ldots)?

Correct answer: (345)

Direct answer: option A, 345. The AP is -5,-1,3,..., so the first term is a=-5 and the common difference is d=4. For 15 terms, the last term is a15=a+14d=-5+14×4=-5+56=51. Now use S_n=n/2(first term+last term): S15=15/2×(-5+51)=15/2×46=15×23=345. Option A, 345, is exactly this result. Option B, 355, usually comes from an arithmetic error in adding the end terms. Option C, 365, may come from mishandling the negative first term or the number of steps. Option D, 375, is also too large and does not satisfy the formula. Although the first terms are negative, later positive terms are larger; the average of the first and last terms is 23, and 15×23=345. Always use n-1 when finding the nth term.