document.write( "Question 429783: What is the 2000th term of the following sequence 8,11,16,23 \n" ); document.write( "
Algebra.Com's Answer #298491 by robertb(5830)\"\" \"About 
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\"a%5Bn%5D-a%5Bn-1%5D+=+2n-1\" is the recursion law.
\n" ); document.write( "Now
\n" ); document.write( "\"a%5Bn-1%5D-a%5Bn-2%5D+=+2n-3\",
\n" ); document.write( "\"a%5Bn-2%5D-a%5Bn-3%5D+=+2n-5\",
\n" ); document.write( "....................
\n" ); document.write( "\"a%5B3%5D-a%5B2%5D+=+5\",
\n" ); document.write( "\"a%5B2%5D-a%5B1%5D+=+3\".
\n" ); document.write( "==> \"a%5Bn%5D+-+a%5B1%5D+=+%282n+-+1%29+%2B+%282n+-+3%29+%2B+%282n+-+5%29+\"+ ...+ \"5+%2B+3\" by adding corresponding sides.
\n" ); document.write( "<==> \"a%5Bn%5D+-+8+=+%28%28n-1%29%2F2%29%2A%283+%2B+%282n-1%29%29\"
\n" ); document.write( "<==> \"a%5Bn%5D+-+8+=+%28%28n-1%29%2F2%29%2A%282n+%2B+2%29+=+%28n-1%29%28n%2B1%29+=+n%5E2+-+1\"
\n" ); document.write( "<==> \"a%5Bn%5D+=+n%5E2+%2B+7\"
\n" ); document.write( "==> \"a%5B2000%5D+=+2000%5E2+%2B+7+=+4000007\"
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