document.write( "Question 1173732: The sum of 8terms on AP is 160 while the sum of 20 terms is 880 find
\n" ); document.write( "The 43rd tert
\n" ); document.write( "The sum of 12 terms
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Algebra.Com's Answer #799050 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The sum of 8 terms is 160, so the average of the 8 terms is 160/8=20.

\n" ); document.write( "The average of the 8 terms is the average of the first term, a, and the 8th term, a+7d:

\n" ); document.write( " $\"%28a%2B%28a%2B7d%29%29%2F2+=+20\"$
\n" ); document.write( " $\"2a%2B7d+=+40\"$ (1)

\n" ); document.write( "The sum of 20 terms is 880, so the average of the 20 terms is 880/20 = 44.

\n" ); document.write( "The average of the 20 terms is the average of the first term, a, and the 20th term, a+19d:

\n" ); document.write( " $\"%28a%2B%28a%2B19d%29%29%2F2+=+44\"$
\n" ); document.write( " $\"2a%2B19d+=+88\"$ (2)

\n" ); document.write( "Comparing (1) and (2), we see 12d=48, so the common difference d is 4.

\n" ); document.write( "Then either (1) or (2) tells us that the first term is 6.

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

\n" ); document.write( "43rd term: a+42d = 6+42(4) = 6+168 = 174

\n" ); document.write( "Sum of (first) 12 terms: 12 times the average of the first and 12th:

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