SOLUTION: What is the 2000th term of the following sequence 8,11,16,23

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Question 429783: What is the 2000th term of the following sequence 8,11,16,23
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a%5Bn%5D-a%5Bn-1%5D+=+2n-1 is the recursion law.
Now
a%5Bn-1%5D-a%5Bn-2%5D+=+2n-3,
a%5Bn-2%5D-a%5Bn-3%5D+=+2n-5,
....................
a%5B3%5D-a%5B2%5D+=+5,
a%5B2%5D-a%5B1%5D+=+3.
==> a%5Bn%5D+-+a%5B1%5D+=+%282n+-+1%29+%2B+%282n+-+3%29+%2B+%282n+-+5%29++ ...+ 5+%2B+3 by adding corresponding sides.
<==> a%5Bn%5D+-+8+=+%28%28n-1%29%2F2%29%2A%283+%2B+%282n-1%29%29
<==> a%5Bn%5D+-+8+=+%28%28n-1%29%2F2%29%2A%282n+%2B+2%29+=+%28n-1%29%28n%2B1%29+=+n%5E2+-+1
<==> a%5Bn%5D+=+n%5E2+%2B+7
==> a%5B2000%5D+=+2000%5E2+%2B+7+=+4000007