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

Question 979750: How many terms of the arithmetic sequence 88,85,82,... appears before the number -17 appears?
Answer by ikleyn(52873) (Show Source): You can put this solution on YOUR website!

First term of the given arithmetic progression is = 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

= - = -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 = ,
n-1 = 35,
n = 36.

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

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