SOLUTION: 8,4,4,4,1/2,1/4,1/8..... Can you guest what the next term is(the 8th term)? Now can you make a formula which will tell you what the 100th term is? I guess the next term is 1/1

Algebra ->  Sequences-and-series -> SOLUTION: 8,4,4,4,1/2,1/4,1/8..... Can you guest what the next term is(the 8th term)? Now can you make a formula which will tell you what the 100th term is? I guess the next term is 1/1      Log On


   

Question 48068: 8,4,4,4,1/2,1/4,1/8.....
Can you guest what the next term is(the 8th term)? Now can you make a formula which will tell you what the 100th term is?
I guess the next term is 1/16, but I don't know formula to figure out the 100th term.
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
8,4,2,1,1/2,1/4,1/8.....
It seems you got your sequence wrong, but I'll work with what you got.
Ratio = (1/4)/(1/2) = 1/2 Take a preceding divided by the number before it.
Formula: P%28t%29+=+a%28r%5E%28t+-+1%29%29
a = first term
r = ratio
t = term
P%28t%29+=+8%281%2F2%29%5E%28t+-+1%29
8th term:
P%28t%29+=+8%281%2F2%29%5E%288+-+1%29
P%28t%29+=+8%281%2F2%29%5E%287%29+=+1%2F16
100th term:
P%28t%29+=+8%281%2F2%29%5E%28100+-+1%29
P%28t%29+=+8%281%2F2%29%5E%2899%29 About 1.262177448 x 10^-29