document.write( "Question 512608: 5,5,6,8,11,15 what is the 20th term and 21th \n" ); document.write( "
Algebra.Com's Answer #342699 by Edwin McCravy(20060)\"\" \"About 
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document.write( "          1st          2nd  \r\n" );
document.write( "n  an  differences differences\r\n" );
document.write( "1   5     0           1               \r\n" );
document.write( "2   5     1           1\r\n" );
document.write( "3   6     2           1  \r\n" );
document.write( "4   8     3           1  \r\n" );
document.write( "5  11     4\r\n" );
document.write( "6  15     \r\n" );
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document.write( "Since the 2nd differences are all constant we try a 2nd\r\n" );
document.write( "degree polynomial in n\r\n" );
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document.write( "\"a%5Bn%5D+=+An%5E2%2BBn%2BC\"\r\n" );
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document.write( "Simplifying:\r\n" );
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document.write( "\"system%285=+A%2BB%2BC%2C+%0D%0A++++++++++5=+4A%2B2B%2BC%2C+%0D%0A++++++++++6=+9A%2B3B%2BC%29\"\"system%28A%2BB%2BC=5%2C+%0D%0A++++++++++4A%2B2B%2BC=5%2C+%0D%0A++++++++++9A%2B3B%2BC=6%29\"\r\n" );
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document.write( "Solve that system and get A = \"1%2F2\", B = \"-3%2F2\", C = 6\r\n" );
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document.write( "So the equation\r\n" );
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document.write( "\"a%5Bn%5D+=+An%5E2%2BBn%2BC\"\r\n" );
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document.write( "becomes:\r\n" );
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document.write( "\"a%5Bn%5D+=+expr%281%2F2%29n%5E2-expr%283%2F2%29n%2B6\"\r\n" );
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document.write( "\"a%5Bn%5D+=+expr%281%2F2%29n%5E2-expr%283%2F2%29n%2B12%2F2\"\r\n" );
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document.write( "\"a%5Bn%5D+=+%28n%5E2-3n%2B12%29%2F2\"\r\n" );
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document.write( "Substituting n = 20\r\n" );
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document.write( "\"a%5B20%5D+=+%2820%5E2-3%2A20%2B12%29%2F2\"\r\n" );
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document.write( "\"a%5B20%5D+=+%28400-60%2B12%29%2F2\"\r\n" );
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document.write( "\"a%5B20%5D+=+352%2F2\"\r\n" );
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document.write( "\"a%5B20%5D+=+176\"\r\n" );
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document.write( "Substituting n = 21\r\n" );
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document.write( "\"a%5B21%5D+=+%2821%5E2-3%2A21%2B12%29%2F2\"\r\n" );
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document.write( "\"a%5B21%5D+=+%28441-63%2B12%29%2F2\"\r\n" );
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document.write( "\"a%5B21%5D+=+390%2F2\"\r\n" );
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document.write( "\"a%5B21%5D+=+195\"\r\n" );
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document.write( "Answers: \"a%5B20%5D+=+176\", \"a%5B21%5D+=+195\"\r\n" );
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document.write( "Edwin
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