document.write( "Question 983310: 1,2,2,4,3,8,7,10 what is next number? \n" ); document.write( "
Algebra.Com's Answer #605041 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "A very common recursion formula is of this form:\r\n" );
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document.write( "\"t%5Bn%2B1%5D=+a%2An%2At%5Bn%5D%2Bb%2An%2Bc\", where a,b, and c are constants:\r\n" );
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document.write( "Substitute n=1\r\n" );
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document.write( "\"t%5B1%2B1%5D=+a%2A1%2At%5B1%5D%2Bb%2A1%2Bc\"\r\n" );
document.write( "\"t%5B2%5D=+a%2A1%2A1%2Bb%2Bc\"\r\n" );
document.write( "\"2=+a%2Bb%2Bc\"\r\n" );
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document.write( "Substitute n=2\r\n" );
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document.write( "\"t%5B2%2B1%5D=+a%2A2%2At%5B2%5D%2Bb%2A2%2Bc\"\r\n" );
document.write( "\"t%5B3%5D=+2a%2A14%2B2b%2Bc\"\r\n" );
document.write( "\"24=+28a%2B2b%2Bc\"\r\n" );
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document.write( "Substitute n=3\r\n" );
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document.write( "\"t%5B3%2B1%5D=+a%2A3%2At%5B3%5D%2Bb%2A3%2Bc\"\r\n" );
document.write( "\"t%5B4%5D=+3a%2A24%2B3b%2Bc\"\r\n" );
document.write( "\"66=+72a%2B3b%2Bc\"\r\n" );
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document.write( "We will find a,b, and c from this system:\r\n" );
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document.write( "\"system%2816a%2Bb%2Bc=14%2C28a%2B2b%2Bc=24%2C72a%2B3b%2Bc-66%29\"\r\n" );
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document.write( "Subtracting the 1st equation from the 2nd equation\r\n" );
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document.write( "\"12a%2Bb=10\"\r\n" );
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document.write( "Subtracting the 2nd equation from the 3rd equation\r\n" );
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document.write( "\"44a%2Bb=42\"\r\n" );
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document.write( "So now we have this system:\r\n" );
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document.write( "\"system%2812a%2Bb=10%2C44a%2Bb=42%29\"\r\n" );
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document.write( "Subtracting the first equation from the second:\r\n" );
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document.write( "\"32a=32\"\r\n" );
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document.write( "\"a=1\"\r\n" );
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document.write( "Substitute in 12a+b=10\r\n" );
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document.write( "12(1)+b=10\r\n" );
document.write( "   12+b=10\r\n" );
document.write( "      b=-2\r\n" );
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document.write( "Substitute in 16a+b+c=14\r\n" );
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document.write( "16(1)+(-2)+c=14\r\n" );
document.write( "      16-2+c=14\r\n" );
document.write( "        14+c=14\r\n" );
document.write( "           c=0\r\n" );
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document.write( "So recursion formula:\r\n" );
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document.write( "\"t%5Bn%2B1%5D=+1%2An%2At%5Bn%5D%2B%28-2%29%2An%2B0\"\r\n" );
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document.write( "\"t%5Bn%2B1%5D=+n%2At%5Bn%5D-2n\"\r\n" );
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document.write( "Now we test the recursion formula to see if \"t%5B5%5D=256\"\r\n" );
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document.write( "\"t%5B4%2B1%5D=+4%2At%5B4%5D-2%2A4\"\r\n" );
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document.write( "\"t%5B5%5D=+4%2A66-8\"\r\n" );
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document.write( "\"t%5B5%5D=+256\"\r\n" );
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document.write( "So this is the correct recursion formula.\r\n" );
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document.write( "So we use it to find \"t%5B6%5D\"\r\n" );
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document.write( "\"t%5B5%2B1%5D=+5%2At%5B5%5D-2%2A5\"\r\n" );
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document.write( "\"t%5B6%5D=+5%2A256-10\"\r\n" );
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document.write( "\"t%5B6%5D=+1270\"   <--answer\r\n" );
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document.write( "Edwin
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