SOLUTION: Determine whether the sequence converges or diverges. If it converges, give the limit. 108, -18, 3, negative one divided by two , .. choices below Converges; 19980 Converg

Algebra ->  Trigonometry-basics -> SOLUTION: Determine whether the sequence converges or diverges. If it converges, give the limit. 108, -18, 3, negative one divided by two , .. choices below Converges; 19980 Converg      Log On


   

Question 1135685: Determine whether the sequence converges or diverges. If it converges, give the limit.
108, -18, 3, negative one divided by two , ..
choices below
Converges; 19980

Converges; 0

Diverges

Converges; six hundred and forty eight divided by five
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


108, -18, 3, -1%2F2
The formula for nth term of an geometric progression is a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29
divide two consecutive terms to find ratio r
r=-18%2F108=-1%2F6
r=3%2F-18=-1%2F6
so, in this example we have a%5B1%5D=108 and r=-1%2F6 so:
then

a%5Bn%5D=108%2A%28-1%2F6%29%5E%28n-1%29
or
a%5Bn%5D=%28-1%29%5E%28n+%2B+1%29+%2A2%5E%283+-+n%29%2A+3%5E%284+-+n%29

lim%28n-%3Einfinity%29+%28-1%29%5E%28-1+%2B+n%29+2%5E%283+-+n%29+3%5E%284+-+n%29+=+0

so, answer is: Converges; 0