SOLUTION: What is the common difference of a 57-term arithmetic sequence where the first term is -25 and the sum is 17,727? 11 11.5 12 12.5

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Question 772954: What is the common difference of a 57-term arithmetic sequence where the first term is -25 and the sum is 17,727?

11
11.5
12
12.5
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Your general term is %28-25%29%2B%28n-1%29%2Ad with common difference d, and for the sum of the terms,
%28n%2F2%29%28%28-25%29%2BLastTerm%29=17727

For the LastTerm, you know n=57 but still not know d. This term is like, %28-25%29%2B%2857-1%29d

Put this all into the sum equation and as n=57.
highlight%28%2857%2F2%29%28%28-25%29%2B%28%28-25%29%2B%2857-1%29d%29%29=17727%29
Solve for d.