document.write( "Question 1151124: Three positive numbers form an arithmetic progression; their sum is 18. If the first number is increased by 4, then the numbers will form a geometric progression. Find the original three numbers in arithmetic progression.
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Algebra.Com's Answer #772750 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Three positive numbers form an arithmetic progression; their sum is 18. If the first number is increased by 4,
\n" ); document.write( "then the numbers will form a geometric progression. Find the original three numbers in arithmetic progression.
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document.write( "Since the three numbers form an AP with the sum 18, the middle terms is 18/3 = 6.\r\n" );
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document.write( "Let \"d\" be the common difference of this AP.\r\n" );
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document.write( "Then the three terms of the AP are  6-d, 6 and 6+d.\r\n" );
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document.write( "Then the three terms of the GP are  ((6-d)+4) = 10-d, 6 and 6+d.\r\n" );
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document.write( "Since the terms  10-d, 6 and 6+d  form a GP,\r\n" );
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document.write( "     = .\r\n" );
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document.write( "It is your equation to find \"d\". Cross multiply\r\n" );
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document.write( "    6d = (10-d)*(6+d)\r\n" );
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document.write( "    6d = 60 - 6d + 10d - d^2\r\n" );
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document.write( "    d^2 + 2d - 60 = 0\r\n" );
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document.write( "     =  =  = .\r\n" );
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document.write( "With the middle term 6,  NEITHER  value of  d =  = 6.81...  NOR   d =  = -8.81...\r\n" );
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document.write( "provides three positive terms of the AP.\r\n" );
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document.write( "ANSWER.  As the problem is worded, printed, posted and presented, the solution DOES NOT exist.\r\n" );
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