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Question: Find the sum of the arithmetic series with the following characteristics: a1= 16, d = –9, n = 18
Asked by alex10
The sum S of an arithmetic series is given by the formula: S = n/2 * (a1 + an) where n is the number of terms, a1 is the first term, and an is the last term. We already know n, a1, and the common difference d. The nth term of an arithmetic sequence an is found by the formula an = a1 + (n - 1) * d. Let's calculate the last term first: an = a1 + (n - 1) * d an = 16 + (18 - 1) * -9 an = 16 - 9 * 17 an = 16 - 153 an = -137 Now we can calculate the sum S: S = 18/2 * (16 + (-137)) S = 9 * (-121) S = -1089 Therefore, the sum of the arithmetic series is -1089.
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