document.write( "Question 823755: I need detail solution of this question:
\n" ); document.write( "The first term of an arithmetic progression is 8. The sum of the first 10 terms of this progression
\n" ); document.write( "divided by the sum of the first 5 terms is 3.25. How many terms of this progression add up
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Algebra.Com's Answer #495769 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
I need detail solution of this question:
\n" ); document.write( "The first term of an arithmetic progression is 8.
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document.write( "a1=8\r\n" );
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The sum of the first 10 terms of this progression...
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document.write( "Sn = \"n%2F2\"[2a1 + (n-1)d]\r\n" );
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document.write( "S10 = \"10%2F2\"[2(8) + (10-1)d] =\r\n" );
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document.write( "                 5[16 + 9d] =\r\n" );
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document.write( "                 80 + 45d\r\n" );
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...divided by...\r
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document.write( "Sn = \"n%2F2\"[2a1 + (n-1)d]\r\n" );
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document.write( "S5 = \"5%2F2\"[2(8) + (5-1)d] =\r\n" );
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document.write( "                \"5%2F2\"[16 + 4d] =\r\n" );
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document.write( "                 40 + 10d\r\n" );
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...is 3.25:
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document.write( "\"%2880+%2B+45d%29%2F%2840+%2B+10d%29\" = 3.25  [Note: 3.25=\"3%261%2F4\"=\"13%2F4\" ]\r\n" );
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document.write( "\"%2880+%2B+45d%29%2F%2840+%2B+10d%29\" = \"13%2F4\"\r\n" );
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document.write( "Cross-multiply:\r\n" );
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document.write( "4(80 + 45d) = 13(40 + 10d)\r\n" );
document.write( " 320 + 180d = 520 + 130d\r\n" );
document.write( "        50d = 200\r\n" );
document.write( "          d = 4 \r\n" );
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How many terms of this progression add up to 1620?
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document.write( "Sn = \"n%2F2\"[2a1 + (n-1)d]\r\n" );
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document.write( "1620 = \"n%2F2\"[2(8) + (n-1)4]\r\n" );
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document.write( "1620 = \"n%2F2\"[16 + 4(n-1)]\r\n" );
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document.write( "11620 = \"n%2F2\"[16 + 4n - 4]\r\n" );
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document.write( "1620 = \"n%2F2\"[12 + 4n]\r\n" );
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document.write( "1620 = 6n + 2nē\r\n" );
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document.write( "   0 = 2nē + 6n - 1620\r\n" );
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document.write( "Divide every term by 2\r\n" );
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document.write( "   0 = nē + 3n - 810\r\n" );
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document.write( "   0 = (n-27)(n+30)\r\n" );
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document.write( "    n-27=0;    n+30=0\r\n" );
document.write( "       n=27;      n=-30 (ignore)\r\n" );
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document.write( "Answer:  27 terms add up to 1620.\r\n" );
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document.write( "Edwin
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