SOLUTION: The first term of an arithmetic series is -12 and the last term is 22. The sum of all the terms of the series is 260. Find the common difference of the series.

Algebra ->  Sequences-and-series -> SOLUTION: The first term of an arithmetic series is -12 and the last term is 22. The sum of all the terms of the series is 260. Find the common difference of the series.      Log On


   

Question 1136300: The first term of an arithmetic series is -12 and the last term is 22. The sum of all the terms of the series is 260. Find the common difference of the series.
Answer by greenestamps(13203) About Me  (Show Source):
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The sum of all the terms of an arithmetic series is the number of terms, multiplied by the average of the first and last terms. From the given information,

n%28%28-12%2B22%29%2F2%29+=+260
5n+=+260
n+=+52

There are 52 terms in the sequence. The 52nd term is the first term plus the common difference 51 times:

22+=+-12%2B51d
34+=+51d
d+=+34%2F51+=+2%2F3

The common difference in the series is 2/3.