document.write( "Question 1096580: Geometric Series Question:\r
\n" ); document.write( "\n" ); document.write( "a, a-12, a+12 are the first three terms of a geometric sequence\r
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Algebra.Com's Answer #711011 by ikleyn(52797)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Since a, a-12 and a+12 are three consecutive terms of an geometric progression, you have\r\n" );
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document.write( "\"%28a-12%29%2Fa\" = \"%28a%2B12%29%2F%28a-12%29\".      ( the ratio  \"a%5B2%5D%2Fa%5B1%5D\"  is the same as the ratio  \"a%5B3%5D%2Fa%5B2%5D\" )\r\n" );
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document.write( "Then cross-nultiplying\r\n" );
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document.write( "\"%28a-12%29%5E2\" = a*(a+12)  ====>\r\n" );
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document.write( "a^2 - 24a + 144 = a^2 + 12a  ====>\r\n" );
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document.write( "-24a + 144 = 12a  ====>  144 = 24a + 12a  ====>  144 = 36a  ====>  a = \"144%2F36\" = 4.\r\n" );
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document.write( "Your GP is  4, 4-12 = -8,  4+12 = 16.\r\n" );
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document.write( "It has the first term 4 and the common difference (-2).\r\n" );
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\n" ); document.write( "There is a bunch of lessons on geometric progressions in this site\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( "    - One characteristic property of geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Fresh, sweet and crispy problem on arithmetic and geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Mathematical induction and geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Mathematical induction for sequences other than arithmetic or geometric\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 \"Geometric 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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