text: math genesis needed again...?  you will have my many thanks!!!? find the sum of the first 38 terms of the arithmetic sequence with the first term 2 and thirty -eight term 113. the formula for finding the nth term of an arithmetic sequence is  an = a1 + (n - 1)d  you need the spacing, d:  113 = 2 + (38 - 1)d 111 = 37d d = 3  the formula for finding the sum of the sequence is  s = n[2a1 + (n - 1)d] / 2 = 38[2(2) + (38 - 1)3] /2 = 38(4 + 111)/2 = 38(115)/2 = 2185