document.write( "Question 1036257: In an A.P, the sum of three positive consecutive numbers is 21. The sum of their squares is 155.Find the numbers \n" ); document.write( "

Algebra.Com's Answer #650899 by ikleyn(52788) $\"\"$ $\"About$

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.In an A.P, the sum of three positive consecutive numbers is 21. The sum of their squares is 155.Find the numbers
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document.write( "Let x be the middle term of the AP (the second term) and d be the common difference.\r\n" );
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document.write( "Then the three terms are x-d, x, and x+d, and their sum is 3x = 21 --->  x  =  = 7. \r\n" );
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document.write( "The second condition is \r\n" );
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document.write( " = 155,\r\n" );
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document.write( "which gives \r\n" );
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document.write( " = 155, \r\n" );
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document.write( "147 + 2d^2 = 155,\r\n" );
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document.write( "2d^2 = 155 - 147 = 8,  --->  d^2 = 4  --->  d = +/-2.\r\n" );
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document.write( "So, the progression is  5, 7, 9  or  9, 7, 5.\r\n" );
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document.write( "Answer. {5, 7, 9}  or  {9, 7, 5}.\r\n" );
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