document.write( "Question 1107256: 3;5;11;21
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Algebra.Com's Answer #722293 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "n       diff      diff(diff)\r\n" );
document.write( "1     3                 \r\n" );
document.write( "2     5       2                    \r\n" );
document.write( "3    11       6           4\r\n" );
document.write( "4    21      10           4\r\n" );
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\n" ); document.write( "\n" ); document.write( "So if we assume $\"+a%5Bn%5D+=+k%5B1%5Dn%5E2+%2B+k%5B2%5Dn+%2B+k%5B3%5D+\"$
\n" ); document.write( "we can write
\n" ); document.write( "(1) $\"+3+=+k%5B1%5D+%2B+k%5B2%5D+%2B+k%5B3%5D+\"$
\n" ); document.write( "(2) $\"+5+=+k%5B1%5D%282%5E2%29+%2B+k%5B2%5D%282%29+%2B+k%5B3%5D+\"$
\n" ); document.write( "(3) $\"+11+=+k%5B1%5D%283%5E2%29+%2B+k%5B2%5D%283%29+%2B+k%5B3%5D+\"$ \r
\n" ); document.write( "\n" ); document.write( "This system can be solved to get $\"+k%5B1%5D+=+2+\"$ , $\"+k%5B2%5D+=+-4+\"$ , and $\"+k%5B3%5D+=+5+\"$ \r
\n" ); document.write( "\n" ); document.write( "giving $\"+a%5Bn%5D+=+2n%5E2+-4n+%2B+5+\"$ ; n = 1,2,3,Е\r
\n" ); document.write( "\n" ); document.write( "and $\"+highlight%28+a%5B48%5D+=+4421+%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "ЧЧ\r
\n" ); document.write( "\n" ); document.write( "There is probably a method to solve this using z-transforms but I'm very rusty on them.\r
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