SOLUTION: how many terms are in the sequence -83, -66, -49, -32,...597 I think this is an arithmetic sequence, I am just not sure how to calculate how many terms are in this

Algebra ->  Sequences-and-series -> SOLUTION: how many terms are in the sequence -83, -66, -49, -32,...597 I think this is an arithmetic sequence, I am just not sure how to calculate how many terms are in this       Log On


   

Question 983316: how many terms are in the sequence -83, -66, -49, -32,...597
I think this is an arithmetic sequence, I am just not sure how to calculate how many terms are in this
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!

You are given an arithmetic progression with the first term  -83,  with the common difference  17  and with the last term  597.

The number of terms in this progression is  %28597+-+%28-83%29%29%2F17 + 1 = %28597+%2B+83%29%2F17 + 1 = 680%2F17 + 1 = 40 + 1 = 41.

The ratio  %28597+-+%28-83%29%29%2F17  is the number of  intervals  between the terms.  You must add  "1"  to account for the number of  terms.

Or,  in similar situation you may always think about  "an arithmetic progression  1, 2"  consisting of two terms.
It has the common difference  1,  %282-1%29%2F1 = 1  and the progression includes two terms.