SOLUTION: find th eeight term of a sequence whose first three terms are 13,6,-1

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Question 535133: find th eeight term of a sequence whose first three terms are 13,6,-1
Answer by fcabanski(1391) About Me  (Show Source):
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The sequence is a simple arithmetic sequence. Each term is the last term -7.


13, 13-7, 13-7-7, 13-7-7-7...


13, 6, -1, -8, -15, -22, -29, -36


Writing the terms is practical for a few terms, such as 8 (as we just wrote.) But if the problem asked for the 500th term we wouldn't want to write 500 terms. We could find the nth term of the sequence with a simple formula.


nth term = 13-7(n-1).


n=8, the 8th term, it's 13-7(7) = -36.


n=500, the 500th term, it's 13-7(499)=-3480.