document.write( "Question 1175058: find k so that 2k+1, 3k+1 and 5k+1 form a geometric sequence \n" ); document.write( "
Algebra.Com's Answer #800579 by ikleyn(52793)\"\" \"About 
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document.write( "For it, you should have\r\n" );
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document.write( "    \"a%5B3%5D%2Fa%5B2%5D\" = \"a%5B2%5D%2Fa%5B1%5D\",   or\r\n" );
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document.write( "    \"%285k%2B1%29%2F%283k%2B1%29\" = \"%283k%2B1%29%2F%282k%2B1%29\",   or, cross multiplying\r\n" );
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document.write( "    (5k+1)*(2k+1) = \"%283k%2B1%29%5E2\",   or, simplifying\r\n" );
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document.write( "    10k^2 + 7k + 1 = 9k^2 + 6k + 1\r\n" );
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document.write( "    k^2 + k = 0\r\n" );
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document.write( "    k(k+1) = 0\r\n" );
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document.write( "    k= 0  OR  k= -1.\r\n" );
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document.write( "At k= 0,  the three terms of the GP are 1, 1, 1.\r\n" );
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document.write( "At k = -1,  the three terms of the GP are -1, -2, -4.\r\n" );
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document.write( "So, there are 2 possibilities.\r\n" );
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document.write( "One geometric progression is  {1, 1, 1,}.  It corresponds to the value of k= 0.\r\n" );
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document.write( "Another geometric progression is  {-1, -2, -4}.   It corresponds to the value of k= -1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On geometric progressions,  see introductory lessons\r
\n" ); document.write( "\n" ); document.write( "    - Geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for geometric progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Word problems on geometric progressions\r
\n" ); document.write( "\n" ); document.write( "in this site.\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
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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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