Mikaila D. answered • 02/08/18
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The sum of an arithmetic series S_n = (a_1 + a_n)/2 * n
We know a_1 (the first term in the series, 5) and a_n (the last term in the series, 53). We need to find out how many terms are in the sequence. The difference between each term is 3. To find out which term 53 is in the sequence, we use the arithmetic series formula a_n = d(n-1) + a_1
53 = 3(n-1) + 5
48 = 3(n-1)
16 = n-1
17 = n
53 is the 17th term in the sequence, so we will substitute 17 for "n."
S_17 = (5 + 53) / 2 * 17 = 58/2 * 17 = 29 *17 =493
