Question 1162999
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The sum of the terms in an arithmetic sequence is the number of terms, multiplied by the average of the terms.  So the average of all the terms is the sum, divided by the number of terms.<br>
In this problem, the number of terms is 9 and the sum is -135, so the average of the terms is -135/9 = -15.<br>
In an arithmetic sequence of 9 terms, the average of all the terms is the term in the middle -- the 5th term.<br>
So the 5th term in the sequence is -15.<br>
The 5th term is the first term, plus the common difference 4 times:<br>
{{{-15 = 9+4d}}}
{{{4d = -24}}}
{{{d = 6}}}<br>
ANSWER: The common difference is -6<br>