document.write( "Question 1208674: The 10th and 15th terms of an AP are -5 and -15/2 respectively.what is the sum of the first 20 terms \n" ); document.write( "

Algebra.Com's Answer #847067 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The difference between the 10th and 15th terms is (-15/2)-(-5) = (-15/2)+(10/2) = -5/2, so the common difference is (-5/2)/5 = (-1/2).

\n" ); document.write( "The sum of 20 terms of an AP is 20 times the average of the terms.

\n" ); document.write( "In an AP with an even number of terms, the average of all the terms is the average of the two middle terms (10th and 11th terms).

\n" ); document.write( "We were given that the 10th term is -5, and we determined that the common difference is -1/2, so the 11th term is -5-1/2 = -11/2.

\n" ); document.write( "The average of all the terms is then the average of -5 and -11/2:

\n" ); document.write( " $\"%28%28-5%29%2B%28-11%2F2%29%29%2F2=%28-21%2F2%29%2F2=%28-21%2F4%29\"$

\n" ); document.write( "And so the sum of the first 20 terms is $\"20%28-21%2F4%29=5%28-21%29=-105\"$

\n" ); document.write( "ANSWER: -105

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