SOLUTION: Determine the sum of the first 15 terms of an arithmetic series if the middle term is 92.

Question 1106455: Determine the sum of the first 15 terms of an arithmetic series if the middle term is 92.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The middle term of a 15 term sequence is 92 so this is the eighth term.
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The eighth term(92) of this arithmetic sequence is
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92 = a(1) + 7d
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Therefore, the last term is 7 terms further in the sequence, so it is 92 + 7d
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Likewise, the first term is 7 terms before the 8th term, so it is 92 - 7d.
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The sum of the first and last term is (92 - 7d) + (92 + 7d) = 92 + 92 = 184
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The sum of this arithmetic sequence is
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(1/2) * 15 * 184 = 1380
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Note the sum of an arithmetic sequence is (1/2) * n * (x(1) + x(n)), where n is the number of terms, x(1) is the first term and x(n) is the nth term
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