SOLUTION: Write the sum using summation notation, assuming the suggested pattern continues. -9 - 4 + 1 + 6 + ... + 66

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Question 1091574: Write the sum using summation notation, assuming the suggested pattern continues.
-9 - 4 + 1 + 6 + ... + 66
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
You say "assuming the suggested pattern continues," but you've written it such that the sum terminates at 66 (normally one would write "66 + …" if you wanted to continue the pattern beyond 66). Anyway, here is the solution both ways.
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Assuming finite sum ending with 66 (probably what you want):
S = -9 + -4 + 1 + 6 + 11 + … + 61 + 66
This is an arithmetic sequence with a common difference of 5.
In this problem, n=16 so you get highlight%28+S+=+sum%28%285i+-14%29%2C+i=1%2C+16%29+%29
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As an aside, if you wanted the sum itself, it is +S+=+sum%28a%5Bi%5D%2C+i=1%2C+n%29+=++%28n%2F2%29%2A%28a%5B1%5D%2Ba%5Bn%5D%29+
and for this problem that would be ++sum%28%285i+-14%29%2C+i=1%2C+16%29+=+%2816%2F2%29%28-9%2B66%29+=+8%2A57+=+456+
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If you wanted the notation for an infinite sum:
+S+=+sum%28%285i-14%29%2C+i=1%2C+infinity%29+
In this case the sum diverges (goes to infinity) so there is no numerical value.