Math CentralQuandaries & Queries


Question from Leigh, a student:

Find the sum of the first fifteen terms of an arithmetic series if the middle term is 92


Consider the way that Gauss showed us how to sum an arithmetic sequence. You can see an example in our response to a previous question. 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 + 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 + 92 + 7d = 92 + 92 = 184.

Can you now use Gauss' technique to find the sum of the sequence?


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