document.write( "Question 1110320: The sum of three consecutive terms of
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Algebra.Com's Answer #725335 by ikleyn(52797) $\"\"$ $\"About$

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document.write( "Let \"a\" be the middle term of the sequence, so that the three terms are\r\n" );
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document.write( "    a-d, a, a+d,\r\n" );
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document.write( "where d is the common difference of the AP.  Then\r\n" );
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document.write( "   (a-d) + d + (a+d) = 6,\r\n" );
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document.write( "which implies  3a = 6,  a = 2.\r\n" );
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document.write( "Then the second condition becomes\r\n" );
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document.write( "    (a-d)*a*(a+d) = -90,   or\r\n" );
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document.write( "    2*(2-d)*(2+d) = -90,\r\n" );
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document.write( "    4-d^2 = -45  ====>  d^2 = 4 + 45 = 49  ====>  d = +/- = +/-7.\r\n" );
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document.write( "So, the AP is   2-7 = -5,  2,   2+7 = 9,     OR\r\n" );
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document.write( "                2+7 =  9,  2,   2-7 = -5.\r\n" );
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