document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #754087 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "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" ); document.write( " $\"n%28%28-12%2B22%29%2F2%29+=+260\"$
\n" ); document.write( " $\"5n+=+260\"$
\n" ); document.write( " $\"n+=+52\"$

\n" ); document.write( "There are 52 terms in the sequence. The 52nd term is the first term plus the common difference 51 times:

\n" ); document.write( " $\"22+=+-12%2B51d\"$
\n" ); document.write( " $\"34+=+51d\"$
\n" ); document.write( " $\"d+=+34%2F51+=+2%2F3\"$

\n" ); document.write( "The common difference in the series is 2/3. \n" ); document.write( "

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