The sum of an arithmetic sequence can be found using the formula S = n/2(a + l) where S equals sum, n equals # terms, a equals the first term and l equals last term we know enough of these to find the missing pieces S = -15 n = 20 a = 4 -15 = 20/2 (4 + l) now we only have one unknown -15 = 10 (4 + l) -15 = 40 + 10l -55 = 10l l = -5.5 so the last term is -5.5 now we can use anothe formula to find the common difference l = a + (n-1) d so the last term equals the first term (a) plus # terms -1 times (d) the common difference -5.5 = 4 + (20-1) d -9.5 = 19 d d = -.5 so your common difference is -.5