SOLUTION: Find an A.p whose 6th term is 17 and the sum of the first 13th term is 0

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Question 760277: Find an A.p whose 6th term is 17 and the sum of the first 13th term is 0
Answer by malglu(63) About Me  (Show Source):
You can put this solution on YOUR website!
the answers are
the first term = -68#the difference is -17
we know the sixth term is 17. so 17 = fisrt term (a) + 5 * difference(d) (using formula for finding a term of an AP)
we know the sum of the fisrt 13 terms is 0. so 0 = 13/2 (2a + 12d). using the formula for the sum of the fisrt n terms in an AP.
rearrange the fisrt equation to read 17-5d = a, and substitute this into the second equation and rearrange to get d= -17.
substitute this into the fisrt equation to get a=-68