SOLUTION: For each sequence, find a closed formula for the general term, a sub n. a) -2,-8,-18,-32,-50 b)96,94,92,90,88 c)-58,-580,-5800,-58000,-580000

Algebra ->  Sequences-and-series -> SOLUTION: For each sequence, find a closed formula for the general term, a sub n. a) -2,-8,-18,-32,-50 b)96,94,92,90,88 c)-58,-580,-5800,-58000,-580000      Log On


   

Question 1021048: For each sequence, find a closed formula for the general term, a sub n.
a) -2,-8,-18,-32,-50
b)96,94,92,90,88
c)-58,-580,-5800,-58000,-580000
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a) a%5Bn%5D+=+-2n%5E2, which can be verified directly for n = 1, 2, 3, 4, 5...
b) This is an arithmetic sequence, so the general nth formula is a%5Bn%5D+=+a%5B1%5D%2B%28n-1%29d, with a%5B1%5D+=+96 and d = -2
==> a%5Bn%5D+=+96+-2%28n-1%29+=+98-2n for n = 1, 2, 3, 4, 5...

c) This is a geometric sequence, where a%5Bn%5D+=+-58%2A10%5E%28n-1%29 for n = 1, 2, 3, 4, 5...