Question 450583: What is the 35th term of the arithmetic sequence where a1 = 13 and a17 = –35 ?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Arithmetic sequences have a common difference, d. The common difference can be
obtained from:
d = (a_n - a_1)/(n-1)
In this case, n=17:
d = (a_17 - a_1)/(17 - 1) = (-35 - 17)/(17 - 1) = -48/16 = -3
So the sequence can be written:
a_n = 13 - 3(n-1) = 16 - 3n
To find the 35th term, substitute n=35 into the above equation:
a_35 = 16 - 3(35) = -89
Ans: 35th term = -89
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