document.write( "Question 1180646: Which terms of the sequence 2187,729,243.... Is 1รท9\r
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Algebra.Com's Answer #810377 by ikleyn(52797)\"\" \"About 
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document.write( "This sequence is the geometric progression with the first term  2187 = \"3%5E7\"  and the common ratio of  \"1%2F9\".\r\n" );
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document.write( "To find the number of the term  \"1%2F9\"  in this progression,  write an equation for the general term of a GP\r\n" );
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document.write( "    \"a%5Bn%5D\" = \"a%5B1%5D%2Ar%5E%28n-1%29\".\r\n" );
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document.write( "In your case this formula takes the form\r\n" );
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document.write( "    \"1%2F9\" = \"3%5E7%2A%281%2F3%29%5E%28n-1%29\",   or\r\n" );
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document.write( "    \"1%2F3%5E2\" = \"3%5E%287-%28n-1%29%29\".\r\n" );
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document.write( "From this equation\r\n" );
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document.write( "    -2 = 7 - (n-1)\r\n" );
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document.write( "    -2 = 7 - n + 1\r\n" );
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document.write( "    -2 = 8 - n\r\n" );
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document.write( "     n = 8 + 2 = 10.\r\n" );
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document.write( "ANSWER.  \"1%2F9\"  is the 10-th term in this geometric progression.\r\n" );
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document.write( "To check my answer, you may write this sequence of indexes from 7 to -2 inclusive\r\n" );
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document.write( "       7, 6, 5, 4, 3, 2, 1, 0, -1, -2\r\n" );
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document.write( "and count that the index (-2) is the 10-th member in this sequence.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On geometric progressions,  see introductory lessons\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
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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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