SOLUTION: How many terms of the arithmetic sequence 88,85,82,... appears before the number -17 appears?

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Question 979750: How many terms of the arithmetic sequence 88,85,82,... appears before the number -17 appears?
Answer by ikleyn(52867) About Me  (Show Source):
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First term of the given arithmetic progression is  a%5B1%5D = 88  and the  common difference  is  -3.  We need to determine the index of the term which is equal to  -17.

Thus we have an equation

a%5Bn%5D = a%5B1%5D - %28n-1%29%2Ad = -17,     or

88 - 3*(n-1) = -17.

to determine the unknown index  n.

Solve this equation step by step:

88 + 17 = 3*(n-1),
105 = 3*(n-1),
n-1 = 105%2F3,
n-1 = 35,
n = 36.

Answer.  The number  -17  is  36-th term of the given arithmetic progression.