document.write( "Question 1140594: The sum of the first three terms of an AP is twenty four and the sum of there square is two hundred twenty four.find first three terms of AP \n" ); document.write( "

Algebra.Com's Answer #761122 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "The middle term (the 2-nd term) is one third of the sum, i.e. 24/3 = 8.\r\n" );
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document.write( "The first and the third terms then are  (8-d) and (8+d), where \"d\" is the common difference.\r\n" );
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document.write( "Then for \"d\" you have this equation\r\n" );
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document.write( " = 224.\r\n" );
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document.write( "Simplify and solve for d.\r\n" );
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document.write( "64 - 16d + d^2 + 64 + 64 + 16d + d^2 = 224\r\n" );
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document.write( "2d^2 = 224 - 64 - 64 - 64\r\n" );
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document.write( "2d^2 = 32  ====>  d^2 = 32/2 = 16  ====>  d = +/-  = +/- 4.\r\n" );
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document.write( "So, there are two such progressions:  one is for d = 4,  and the three terms are 4, 8 and 12.\r\n" );
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document.write( "The other is for d = -4, and the three terms are the same in the reversed order  12, 8 and 4.\r\n" );
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