document.write( "Question 1134277: The first term of an Ap is-1 and the sum of the first twenty terms is -240 .find the third term \n" ); document.write( "

Algebra.Com's Answer #751615 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The sum of the first 20 terms of an AP is 20 times the average of the first and 20th terms. So if x is the 20th term,

\n" ); document.write( " $\"-240+=+20%28%28-1%2Bx%29%2F2%29\"$
\n" ); document.write( " $\"-240+=+10x-10\"$
\n" ); document.write( " $\"-230+=+10x\"$
\n" ); document.write( " $\"x+=+-23\"$

\n" ); document.write( "The first term is -1; the 20th term -- the first term plus the common difference 19 times -- is -23. So the common difference is

\n" ); document.write( " $\"%28-23-%28-1%29%29%2F19+=+-22%2F19\"$

\n" ); document.write( "(not a very pleasant sequence....)

\n" ); document.write( "The third term is the first term plus the common difference twice:

\n" ); document.write( " $\"-1+%2B+2%28-22%2F19%29+=+%28-19-44%29%2F19+=+-63%2F19\"$ or -3 6/19 \n" ); document.write( "

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