document.write( "Question 155130: I need to know what number comes next in this sequence and why.
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Algebra.Com's Answer #114216 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
Edwin's solution
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document.write( "We make what is called a \"difference table\":\r\n" );
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document.write( "Write the numbers in a row:\r\n" );
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document.write( "            9   73    241    561    1081    1849 \r\n" );
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document.write( "Under that row, subtract each adjacent pair of numbers,\r\n" );
document.write( "placing the difference between and below them.\r\n" );
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document.write( "(73-9=64, so write 64 between and below the pair 9  73,\r\n" );
document.write( " 241-73=168, so write 168 between and below the pair 73   241, etc.) \r\n" );
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document.write( "Like this:\r\n" );
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document.write( "            9   73     241   561    1081    1849 \r\n" );
document.write( "              64    168   320    520     768 \r\n" );
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document.write( "That row is called the row of 1st differences.                    \r\n" );
document.write( "Under that row, again subtract each adjacent pair of numbers,\r\n" );
document.write( "placing the difference between and below them, like this:\r\n" );
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document.write( "            9   73     241   561    1081    1849 \r\n" );
document.write( "              64    168   320    520     768 \r\n" );
document.write( "                 104    152   200     248\r\n" );
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document.write( "That row is called the row of 2nd differences.                  \r\n" );
document.write( "Under that row, again subtract each adjacent pair of numbers,\r\n" );
document.write( "placing the difference between and below them, like this:\r\n" );
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document.write( "            9   73     241   561    1081    1849 \r\n" );
document.write( "              64    168   320    520     768 \r\n" );
document.write( "                 104    152   200     248\r\n" );
document.write( "                     48     48     48\r\n" );
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document.write( "That row is called the row of 3rd differences.\r\n" );
document.write( "Now notice that they are all the same, so we don't need to\r\n" );
document.write( "make any more rows of differences.  So we assume that the next \r\n" );
document.write( "3rd difference, if we had the next number after 1849, would also \r\n" );
document.write( "be a 48, so we write another 48 on the bottom row.\r\n" );
document.write( "(I'll color it red):\r\n" );
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document.write( "            9   73     241   561    1081    1849 \r\n" );
document.write( "              64    168   320    520     768 \r\n" );
document.write( "                 104    152   200     248\r\n" );
document.write( "                     48     48     48     48\r\n" );
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document.write( "Then we work backwards by adding.  Add the 48 to the 248, getting 296,\r\n" );
document.write( "Write that to the right of the 248. (I'll color it red too).\r\n" );
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document.write( "            9   73     241   561    1081    1849 \r\n" );
document.write( "              64    168   320    520     768 \r\n" );
document.write( "                 104    152   200     248    296\r\n" );
document.write( "                     48     48     48     48 \r\n" );
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document.write( "Still working backward, Add the 296 to the 768, getting 1064,\r\n" );
document.write( "Write that to the right of the 768. (I'll color it red too).\r\n" );
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document.write( "            9   73     241   561    1081    1849 \r\n" );
document.write( "              64    168   320    520     768     1064\r\n" );
document.write( "                 104    152   200     248    296\r\n" );
document.write( "                     48     48     48     48\r\n" );
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document.write( "One more step working backwards.  Add 1064 to the 1849, getting\r\n" );
document.write( "2913, write it at the end of the first row, and there is your answer!:\r\n" );
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document.write( "            9   73     241   561    1081    1849     2913  \r\n" );
document.write( "              64    168   320    520     768     1064\r\n" );
document.write( "                 104    152   200     248    296\r\n" );
document.write( "                     48     48     48     48\r\n" );
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document.write( "Answer: The next term is 2913\r\n" );
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document.write( "Edwin

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