document.write( "Question 1136174: If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers \n" ); document.write( "

Algebra.Com's Answer #753920 by ikleyn(52778) $\"\"$ $\"About$

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document.write( "From the condition, the middle term of the three is one third of 24, i.e. 8.\r\n" );
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document.write( "Then the product of the first and the third is  = 55.\r\n" );
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document.write( "You can write it in the form\r\n" );
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document.write( "    (8-d)*(8+d) = 55,\r\n" );
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document.write( "where d is the common difference.\r\n" );
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document.write( "From the last equation,  d^2 = 64 - 55 = 9;  hence,  d = +/- 3.\r\n" );
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document.write( "It gives you two progressions\r\n" );
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document.write( "    5, 8, 11     and   11, 8, 5.\r\n" );
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document.write( "The second progression is the reversed first, and vice versa.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "There is a bunch of lessons on arithmetic progressions in this site:\r
\n" ); document.write( "\n" ); document.write( "    - Arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - One characteristic property of arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on arithmetic progressions \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Arithmetic progressions\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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