document.write( "Question 1117935: Three numbers are in arithmetic progression,their sum is15and their product is 80.Determine the numbers \n" ); document.write( "

Algebra.Com's Answer #733113 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "Let \"x\" be the second term of the AP, and let \"d\" be its common difference.\r\n" );
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document.write( "Then the terms are  a-d,  a and  a+d.\r\n" );
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document.write( "The sum of the three terms is  15, which gives you an equation  3a = 15,  or  a =  = 5.\r\n" );
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document.write( "Next equation, from the condition, is\r\n" );
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document.write( "(5-d)*5*(5+d) = 80,  or  25 - d^2 = 16  ====>  d^2 = 25 - 16 = 9  ====>  d = +/- 3.\r\n" );
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document.write( "Thus there are two arithmetic progressions satisfying the condition.\r\n" );
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document.write( "First AP is  5-3, 5, 5+3,  or  2, 5, 8.\r\n" );
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document.write( "The second AP is  5+3, 5, 5-3,  or  8, 5, 2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\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( "    - Mathematical induction and 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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