document.write( "Question 1197284: Find the 12th term of a Geometric Sequence whose 3rd term is 432 and the 5th term is 15552 \n" ); document.write( "
Algebra.Com's Answer #830515 by ikleyn(52776)\"\" \"About 
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\n" ); document.write( "Find the 12th term of a Geometric Sequence whose 3rd term is 432 and the 5th term is 15552.
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\n" ); document.write( "\n" ); document.write( "            @MathLover1 wrote many symbols, but failed to solve the problem in a right way: \r
\n" ); document.write( "\n" ); document.write( "            she missed one of the two solutions.\r
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\n" ); document.write( "\n" ); document.write( "            So I came to bring a correct solution and correct answer.\r
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document.write( "Since the 3rd and the 5th terms of the geometric progression are given, we write\r\n" );
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document.write( "    \"a%5B5%5D\" = \"a%5B3%5D%2Ar%5E2\",\r\n" );
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document.write( "or\r\n" );
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document.write( "    15552 = \"432%2Ar%5E2\".\r\n" );
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document.write( "From this equation,  \r\n" );
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document.write( "    \"r%5E2\" = \"15552%2F432\" = 36.\r\n" );
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document.write( "Hence,  r = \"sqrt%2836%29\" = +/- 6.\r\n" );
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document.write( "Thus, there are TWO geometric progressions satisfying the given properties:\r\n" );
document.write( "one progression with the common ratio r= 6 and the other progression with the common ratio r= -6.\r\n" );
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document.write( "For the first progression\r\n" );
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document.write( "    \"a%5B12%5D\" = \"a%5B5%5D%2Ar%5E%2812-5%29\" = \"15552%2A6%5E7\" = 4353564672.\r\n" );
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document.write( "For the second progression\r\n" );
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document.write( "    \"a%5B12%5D\" = \"a%5B5%5D%2Ar%5E%2812-5%29\" = \"15552%2A%28-6%29%5E7\" = -4353564672.\r\n" );
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document.write( "Thus there are two answers and two values for the 12-th term: 4353564672 and -4353564672.\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
\n" ); document.write( "\"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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