SOLUTION: The first term of an Ap is-1 and the sum of the first twenty terms is -240 .find the third term

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Question 1134277: The first term of an Ap is-1 and the sum of the first twenty terms is -240 .find the third term
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The sum of the first 20 terms of an AP is 20 times the average of the first and 20th terms. So if x is the 20th term,

-240+=+20%28%28-1%2Bx%29%2F2%29
-240+=+10x-10
-230+=+10x
x+=+-23

The first term is -1; the 20th term -- the first term plus the common difference 19 times -- is -23. So the common difference is

%28-23-%28-1%29%29%2F19+=+-22%2F19

(not a very pleasant sequence....)

The third term is the first term plus the common difference twice:

-1+%2B+2%28-22%2F19%29+=+%28-19-44%29%2F19+=+-63%2F19 or -3 6/19