document.write( "Question 175764: Find all the geometric sequences such that the sum of the first two terms is 2 and the sum of the first three terms is 3.\r
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\n" ); document.write( "a + ar = 2
\n" ); document.write( "a + a(+- 1/√a) = 2\r
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Algebra.Com's Answer #130889 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Find all the geometric sequences such that the sum of the first two terms is 2 and the sum of the first three terms is 3.
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document.write( "You have this system of equations:\r\n" );
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document.write( "\"system%28a%5B1%5D+%2B+a%5B2%5D+=+2%2C%0D%0Aa%5B1%5D+%2B+a%5B2%5D+%2B+a%5B3%5D+=+3%29\"\r\n" );
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document.write( "Now if you subtract the first equations\r\n" );
document.write( "term by term from the second equation\r\n" );
document.write( "you get\r\n" );
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document.write( "\"a%5B3%5D+=+1\"\r\n" );
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document.write( "\"a%5B1%5Dr%5E%283-1%29+=+1\"\r\n" );
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document.write( "\"a%5B1%5Dr%5E2+=+1\"\r\n" );
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document.write( "\"a%5B1%5D+=+1%2Fr%5E2\"\r\n" );
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document.write( "\"a%5B2%5D+=+a%5B1%5Dr+=+%281%2Fr%5E2%29r+=+%281%2Fr%5Ecross%282%29%29cross%28r%29+=+1%2Fr\"\r\n" );
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document.write( "So the first three terms are\r\n" );
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document.write( "\"a%5B1%5D+=+1%2Fr%5E2\"\r\n" );
document.write( "\"a%5B2%5D+=+1%2Fr\"\r\n" );
document.write( "\"a%5B3%5D+=+1\"\r\n" );
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document.write( "and \"a%5Bn%5D\" is given by:\r\n" );
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document.write( "\"a%5Bn%5D+=+a%5B1%5Dr%5E%28n-1%29+=+%281%2Fr%5E2%29%28r%5E%28n-1%29%29+=+r%5E%28n-3%29\"\r\n" );
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document.write( "So all such geometric sequences are of the form:\r\n" );
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document.write( "\"1%2Fr%5E2\", \"1%2Fr\", \"1\", \"r\", \"r%5E2\", \"r%5E3\",···,\"r%5E%28n-3%29\",···\r\n" );
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document.write( "Edwin

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