SOLUTION: Find the sum of 15 terms of an arithmetic series if the middle term is 92

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Question 1151010: Find the sum of 15 terms of an arithmetic series if the middle term is 92
Answer by MathLover1(20849) About Me  (Show Source):
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Consider the way that Gauss showed us how to sum an arithmetic sequence.
Your example is an arithmetic sequence so there is some number d that you add to each term to obtain the next term.
The middle term of a 15 term sequence is 92; so, this is the 8th term.
The last term is 7 terms further along in the sequence so it is 92+%2B+7d.
Likewise the first term is 7 terms before the 8th term so it is 92+-+7d.
Thus the sum of the first and last term is 92+-+7d+%2B+92+%2B+7d+=+92+%2B+92+=+184
now use Gauss' technique to find the sum of the sequence
S=%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29 where n=number of terms, a%5B1%5D=first term, and a%5Bn%5D=last term
S=%2815%2F2%29%28184%29
S=15%2A92
S=1380