document.write( "Question 1011947: What are next two terms of sequence:
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Algebra.Com's Answer #627953 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
-1,2,12,40,.......
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document.write( "We find a recursion formula of the form:\r\n" );
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document.write( "\"a%5Bn%2B2%5D\"\"%22%22=%22%22\"\"p%2Aa%5Bn%2B1%5D%2Bq%2Aa%5Bn%5D\", where \"a%5B1%5D\"\"%22%22=%22%22\"\"-1\" and \"a%5B2%5D\"\"%22%22=%22%22\"\"2\"\r\n" );
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document.write( "and where p and q are constants:\r\n" );
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document.write( "\"a%5B1%2B2%5D\"\"%22%22=%22%22\"\"pa%5B1%2B1%5D%2Bqa%5B1%5D\"\r\n" );
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document.write( "\"a%5B3%5D=pa%5B2%5D\"\"%22%22=%22%22\"\"qa%5B1%5D\"\r\n" );
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document.write( "\"12=p%2A%282%29\"\"%22%22=%22%22\"\"q%2A%28-1%29\"\r\n" );
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document.write( "\"12\"\"%22%22=%22%22\"\"2p-q\"\r\n" );
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document.write( "(1)   \"2p-q\"\"%22%22=%22%22\"\"12\"\r\n" );
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document.write( "\"a%5B2%2B2%5D\"\"%22%22=%22%22\"\"pa%5B2%2B1%5D%2Bqa%5B2%5D\"\r\n" );
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document.write( "\"a%5B4%5D=pa%5B3%5D%2Bqa%5B2%5D\"\r\n" );
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document.write( "\"40\"\"%22%22=%22%22\"\"p%2A%2812%29%2Bq%2A%282%29\"\r\n" );
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document.write( "\"40\"\"%22%22=%22%22\"\"12p%2B2q\"\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "\"20\"\"%22%22=%22%22\"\"6p%2Bq\"\r\n" );
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document.write( "(2)   \"6p%2Bq\"\"%22%22=%22%22\"\"20\"\r\n" );
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document.write( "Solve the system of equations (1) and (2)\r\n" );
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document.write( "\"system%282p-q=12%2C6p%2Bq=20%29\"\r\n" );
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document.write( "Add the two equations:\r\n" );
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document.write( "\"8p\"\"%22%22=%22%22\"\"32\"\r\n" );
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document.write( "\"p\"\"%22%22=%22%22\"\"4\"\r\n" );
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document.write( "substitute in (1)\r\n" );
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document.write( "(1)   \"2p-q\"\"%22%22=%22%22\"\"12%7D%7D%0D%0A++++++%7B%7B%7B2%284%29-q\"\"%22%22=%22%22\"\"12%7D%7D%0D%0A++++++%7B%7B%7B8-q\"\"%22%22=%22%22\"\"12\"\r\n" );
document.write( "      \"-q\"\"%22%22=%22%22\"\"4\"\r\n" );
document.write( "      \"q\"\"%22%22=%22%22\"\"-4\"\r\n" );
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document.write( "So the recursion formula is\r\n" );
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document.write( " \"a%5Bn%2B2%5D\"\"%22%22=%22%22\"\"pa%5Bn%2B1%5D%2Bqa%5Bn%5D\", where \"a%5B1%5D\"\"%22%22=%22%22\"\"-1\" and \"a%5B2%5D\"\"%22%22=%22%22\"\"2\"\r\n" );
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document.write( "becomes\r\n" );
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document.write( "\"a%5Bn%2B2%5D\"\"%22%22=%22%22\"\"4a%5Bn%2B1%5D-4a%5Bn%5D\", where \"a%5B1%5D\"\"%22%22=%22%22\"\"-1\" and \"a%5B2%5D\"\"%22%22=%22%22\"\"2\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"a%5Bn%2B2%5D\"\"%22%22=%22%22\"\"4%28a%5Bn%2B1%5D-a%5Bn%5D%29\", where \"a%5B1%5D\"\"%22%22=%22%22\"\"-1\" and \"a%5B2%5D\"\"%22%22=%22%22\"\"2\" \r\n" );
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document.write( "Substitute n=1 as a check\r\n" );
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document.write( "\"a%5Bn%2B2%5D\"\"%22%22=%22%22\"\"4%28a%5Bn%2B1%5D-a%5Bn%5D%29\"\r\n" );
document.write( "\"a%5B1%2B2%5D\"\"%22%22=%22%22\"\"4%28a%5B1%2B1%5D-a%5B1%5D%29\"\r\n" );
document.write( "\"a%5B3%5D\"\"%22%22=%22%22\"\"4%28a%5B2%5D-a%5B1%5D%29\"\r\n" );
document.write( "\"a%5B3%5D\"\"%22%22=%22%22\"\"4%28%282%29%5E%22%22-%28-1%29%29\"\r\n" );
document.write( "\"a%5B3%5D\"\"%22%22=%22%22\"\"4%282%2B1%29\"\r\n" );
document.write( "\"a%5B3%5D\"\"%22%22=%22%22\"\"4%283%29\"\r\n" );
document.write( "\"a%5B3%5D\"\"%22%22=%22%22\"\"12\"\r\n" );
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document.write( "Substitute n=2 as a check\r\n" );
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document.write( "\"a%5Bn%2B2%5D\"\"%22%22=%22%22\"\"4%28a%5Bn%2B1%5D-a%5Bn%5D%29\"\r\n" );
document.write( "\"a%5B2%2B2%5D\"\"%22%22=%22%22\"\"4%28a%5B2%2B1%5D-a%5B2%5D%29\"\r\n" );
document.write( "\"a%5B4%5D\"\"%22%22=%22%22\"\"4%28a%5B3%5D-a%5B2%5D%29\"\r\n" );
document.write( "\"a%5B4%5D\"\"%22%22=%22%22\"\"4%28%2812%29%5E%22%22-%282%29%29\"\r\n" );
document.write( "\"a%5B3%5D\"\"%22%22=%22%22\"\"4%2812-2%29\"\r\n" );
document.write( "\"a%5B3%5D\"\"%22%22=%22%22\"\"4%2810%29\"\r\n" );
document.write( "\"a%5B3%5D\"\"%22%22=%22%22\"\"40\"\r\n" );
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document.write( "Substitute n=3:\r\n" );
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document.write( "\"a%5Bn%2B2%5D\"\"%22%22=%22%22\"\"4%28a%5Bn%2B1%5D-a%5Bn%5D%29\"\r\n" );
document.write( "\"a%5B3%2B2%5D\"\"%22%22=%22%22\"\"4%28a%5B3%2B1%5D-a%5B3%5D%29\"\r\n" );
document.write( "\"a%5B5%5D\"\"%22%22=%22%22\"\"4%28a%5B4%5D-a%5B3%5D%29\"\r\n" );
document.write( "\"a%5B5%5D\"\"%22%22=%22%22\"\"4%28%2840%29%5E%22%22-%2812%29%29\"\r\n" );
document.write( "\"a%5B3%5D\"\"%22%22=%22%22\"\"4%2840-12%29\"\r\n" );
document.write( "\"a%5B3%5D\"\"%22%22=%22%22\"\"4%2828%29\"\r\n" );
document.write( "\"a%5B3%5D\"\"%22%22=%22%22\"\"112\"\r\n" );
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document.write( "Substitute n=4\r\n" );
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document.write( "\"a%5Bn%2B2%5D\"\"%22%22=%22%22\"\"4%28a%5Bn%2B1%5D-a%5Bn%5D%29\"\r\n" );
document.write( "\"a%5B4%2B2%5D\"\"%22%22=%22%22\"\"4%28a%5B4%2B1%5D-a%5B4%5D%29\"\r\n" );
document.write( "\"a%5B6%5D\"\"%22%22=%22%22\"\"4%28a%5B5%5D-a%5B4%5D%29\"\r\n" );
document.write( "\"a%5B6%5D\"\"%22%22=%22%22\"\"4%28%28112%29%5E%22%22-%2840%29%29\"\r\n" );
document.write( "\"a%5B6%5D\"\"%22%22=%22%22\"\"4%28112-40%29\"\r\n" );
document.write( "\"a%5B6%5D\"\"%22%22=%22%22\"\"4%2872%29\"\r\n" );
document.write( "\"a%5B6%5D\"\"%22%22=%22%22\"\"288\"\r\n" );
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document.write( "So the sequence goes:\r\n" );
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document.write( "-1,2,12,40,112,288,704,1664,3840,8704,.......\r\n" );
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document.write( "Edwin
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