SOLUTION: Determine whether the sequence converges or diverges. If it converges, give the limit. 108, -18, 3, -1/2 ... Please help me fast , I need the answer super fast! Also could

Algebra ->  Sequences-and-series -> SOLUTION: Determine whether the sequence converges or diverges. If it converges, give the limit. 108, -18, 3, -1/2 ... Please help me fast , I need the answer super fast! Also could      Log On


   

Question 1092175: Determine whether the sequence converges or diverges. If it converges, give the limit.
108, -18, 3, -1/2 ...

Please help me fast , I need the answer super fast! Also could you please explain the answer.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Super fast? Is the test almost over?
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Just by inspection you can see that the terms are getting smaller spiraling around zero.
So your intuition should tell you that it's converging.
Compare successive terms,
-18%2F108=-1%2F6
3%2F-18=-1%2F6
Looks like a pattern.
Each successive term is the previous term multiplied by -1%2F6
It's a geometric progression.
a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29
a%5Bn%5D=108%28-1%2F6%29%5E%28n-1%29
a%5Bn%5D=108%28-6%29%28-1%2F6%29%5E%28n%29
a%5Bn%5D=-648%2F%28-6%29%5En
So when,
n=1,a%5Bn%5D=-648%2F%28-6%29=108
n=2,a%5Bn%5D=-648%2F%28-6%29%5E2=-18
n=3,a%5Bn%5D=-648%2F%28-6%29%5E3=3
n=4,a%5Bn%5D=-648%2F%28-6%29%5E4=-1%2F2
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So that checks out.
In the limit as n-%3Einfinity, a%5Bn%5D-%3E0
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Time up? or on time?