SOLUTION: The least integer in a list of consecutive odd integers is -35. If the sum is 37 how many integers are in the list

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Question 883345: The least integer in a list of consecutive odd integers is -35. If the sum is 37 how many integers are in the list
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
General term of sequence is -35%2B%28n-1%29%2A2=-35%2B2n-2=-37%2B2n.

The sum of some consecutive n terms is 37.
%28n%2F2%29%28-35%2B%282n-37%29%29=37, half of n time the sum of first and last terms;
%28n%2F2%29%282n-72%29=37
n%28n-36%29=37
n%5E2-36n=37
highlight_green%28n%5E2-36n-37=0%29
Easily factored:
%28n-37%29%28n%2B1%29=0

The answer having meaning is n=37.

CHECK:
%2837%2F2%29%28-35%2B2%2A37-37%29
%2837%2F2%29%2874-35-37%29
%2837%2F2%29%282%29
37.
This works.

37 terms of the sequence summed