SOLUTION: The system is defined recursively. Write the first four terms. a1=-5;an=n-an-1

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Question 1059586: The system is defined recursively. Write the first four terms.
a1=-5;an=n-an-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B1%5D+=+-5 and a%5Bn%5D+=+n+-+a%5Bn-1%5D are given to us.


First term:
a%5B1%5D+=+-5
Given; no need to do any work here


Second term:
a%5Bn%5D+=+n+-+a%5Bn-1%5D
a%5B2%5D+=+2+-+a%5B2-1%5D Replace every n with 2
a%5B2%5D+=+2+-+a%5B1%5D
a%5B2%5D+=+2+-+%28-5%29 Replace a1 with -5 (see above)
a%5B2%5D+=+2+%2B+5
a%5B2%5D+=+7
second term = 7


Third term:
a%5Bn%5D+=+n+-+a%5Bn-1%5D
a%5B3%5D+=+3+-+a%5B3-1%5D Replace every n with 3
a%5B3%5D+=+3+-+a%5B2%5D
a%5B3%5D+=+3+-+7 Replace a2 with 7 (see above)
a%5B3%5D+=+-4
third term = -4


Fourth term:
a%5Bn%5D+=+n+-+a%5Bn-1%5D
a%5B4%5D+=+4+-+a%5B4-1%5D Replace every n with 4
a%5B4%5D+=+4+-+a%5B3%5D
a%5B4%5D+=+4+-+%28-4%29 Replace a3 with -4 (see above)
a%5B4%5D+=+4+%2B+4
a%5B4%5D+=+8
fourth term = 8



Summary:
First term = -5
Second term = 7
Third term = -4
Fourth term = 8

The first four terms are: -5, 7, -4, 8