document.write( "Question 1135842: The sum of three terms of an A.P. is 21 and the product of the first and third exceeds the second term by 6, find the terms. \n" ); document.write( "

Algebra.Com's Answer #753531 by ikleyn(52797) $\"\"$ $\"About$

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document.write( "Let x be the middle term .  \r\n" );
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document.write( "Then   = x - d,   = x + d.\r\n" );
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document.write( "Also,   +  +  = (x-d) + x + (x+d) = 3x,  \r\n" );
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document.write( "therefore the first statement of the condition means that\r\n" );
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document.write( "    3x = 21,  which  implies  x =  = 21/3 = 7.\r\n" );
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document.write( "The second statement of the condition means then that\r\n" );
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document.write( "    . = (7-d)*(7+d) = 7 + 6 = 13,   or\r\n" );
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document.write( "     = 13  ====>   = 49 - 13 = 36  ====>  d =  = +/- 6.\r\n" );
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document.write( "So, the three terms of the progression are EITHER\r\n" );
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document.write( "    7 - 6 = 1, 7, 7 + 6 = 13\r\n" );
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document.write( "OR in reverse order\r\n" );
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document.write( "    13, 7, 1.\r\n" );
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