document.write( "Question 1151205: in an A.P the 8th term is twice the 4th term and the 20th term is 40 .find the common difference and the sum of terms from the 8th to the 20th. \n" ); document.write( "

Algebra.Com's Answer #772868 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "in an A.P the 8th term is twice the 4th term and the 20th term is 40.
\n" ); document.write( "find the common difference and the sum of terms from the 8th to the 20th.
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document.write( "From the first part of the condition,\r\n" );
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document.write( "    a + 7d = 2*(a + 3d),\r\n" );
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document.write( "where \"a\" is the 1-st term of the AP and \"d\" is the common difference.\r\n" );
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document.write( "From this equation\r\n" );
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document.write( "    a + 7d = 2a + 6d,\r\n" );
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document.write( "    7d - 6d = 2a - a\r\n" );
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document.write( "     d      = a.      (1)\r\n" );
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document.write( "We are given also\r\n" );
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document.write( "     a + 19d = 40,\r\n" );
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document.write( "which implies, due to (1)\r\n" );
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document.write( "     20d = 40,\r\n" );
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document.write( "       d = a = 2.\r\n" );
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document.write( "Thus, in this AP the first term is 2 and the common difference is 2, too.\r\n" );
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document.write( "So, the 8-th term is  2+2*7 = 16  and  the 20-th term is  40  (given (!) ).\r\n" );
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document.write( "The average of the 8-th term and the 20-th term is, therefore,   = 28.\r\n" );
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document.write( "The sum of the terms from the 8-th term to 20-th term (inclusive) is the product of this mean value 28 \r\n" );
document.write( "by the number of terms, which is (20-7) = 13.\r\n" );
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document.write( "Thus the sum is 28*13 = 364.    ANSWER\r\n" );
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