document.write( "Question 669541: the sum of first 10 terms of an AP is -80 and sum of next 10 terms is -280.find the A.P
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Algebra.Com's Answer #416431 by Edwin McCravy(20056)\"\" \"About 
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the sum of first 10 terms of an AP is -80
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document.write( "The sum formula for the first n terms of an AP is:\r\n" );
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document.write( "Sn = \"n%2F2\"[2a1 + (n-1)·d]\r\n" );
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document.write( "n = 10, Sn = -80\r\n" );
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document.write( "-80 = \"10%2F2\"[2a1 + (10-1)·d]\r\n" );
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document.write( "-80 = 5·[2a1 + 9d]\r\n" );
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document.write( "Dividing through by 5,\r\n" );
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document.write( "-16 = 2a1 + 9d \r\n" );
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\n" ); document.write( "and sum of next 10 terms is -280.
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document.write( "Therefore the sum of the first 20 terms is the sum\r\n" );
document.write( "of the first 10 terms which is -80 PLUS the sum of\r\n" );
document.write( "the next 10 terms, which is given to be -280.  That \r\n" );
document.write( "makes the sum of the first 20 terms -80-280 = -360.\r\n" );
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document.write( "So now we have\r\n" );
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document.write( "Sn = \"n%2F2\"[2a1 + (n-1)·d], this time with\r\n" );
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document.write( "n = 20, Sn = -360\r\n" );
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document.write( "-360 = \"20%2F2\"[2a1 + (20-1)·d]\r\n" );
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document.write( "-360 = 10·[2a1 + 19d]\r\n" );
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document.write( "Dividing through by 10,\r\n" );
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document.write( "-36 = 2a1 + 19d \r\n" );
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document.write( "So we have this system of equations:\r\n" );
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document.write( "-16 = 2a1 +  9d\r\n" );
document.write( "-36 = 2a1 + 19d\r\n" );
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document.write( "Subtracting those two equations term by term,\r\n" );
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document.write( " 20 = -10d\r\n" );
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document.write( " -2 = d\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "-16 = 2a1 + 9d\r\n" );
document.write( "-16 = 2a1 + 9(-2)\r\n" );
document.write( "-16 = 2a1 - 18\r\n" );
document.write( "  2 = 2a1\r\n" );
document.write( "  1 = a1\r\n" );
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document.write( "The AP then is:\r\n" );
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document.write( "1, -1, -3, -5, -7, -9, -11, -13, -15, -17, -19,\r\n" );
document.write( "-21, -23, -25, -27, -29, -31, -33, -35, -37, -39, -41,\r\n" );
document.write( "-43, -45, -47, -49, -51, -53, -55, -57, -59, -61, -63,\r\n" );
document.write( "-65, -67, -69, -71, -73, -75, -77, -79, -81, -83, -85,\r\n" );
document.write( "-87, -89, -91, -93, -95, -97, -99, -101, -103, -105, -107,\r\n" );
document.write( "-109, -111, -113, -115, -117, -119, -121, -123, -125, -127, -129,\r\n" );
document.write( "-131, -133, -135, -137, -139, -141, -143, -145, -147, -149, -151,\r\n" );
document.write( "-153, -155, -157, -159, -161, -163, -165, -167, -169, -171, -173,\r\n" );
document.write( "-175, -177, -179, -181, -183, -185, -187, -189, -191, -193, -195,\r\n" );
document.write( "-197, ... \r\n" );
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document.write( "Edwin
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