SOLUTION: What is the next term in the geometric sequence 16,-4,1,-1/4,.....I have the answer just need to know how to get the answer

Algebra ->  Sequences-and-series -> SOLUTION: What is the next term in the geometric sequence 16,-4,1,-1/4,.....I have the answer just need to know how to get the answer      Log On


   

Question 222954: What is the next term in the geometric sequence 16,-4,1,-1/4,.....I have the answer just need to know how to get the answer
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If a sequence is a geometric sequence then the ratios of all pairs of consecutive terms are the same:
%28-4%29%2F16+=+1%2F%28-4%29+=+%28-1%2F4%29%2F1+=+%28-1%29%2F4
Let's call the next term x. So x%2F%28%28-1%29%2F4%29 must also be equal to %28-1%29%2F4. So all we need to do is solve:
x%2F%28%28-1%29%2F4%29+=+%28-1%29%2F4
Since this is a proportion (one fraction equals another), we can "cross multiply":
x%2A4+=+%28%28-1%29%2F4%29%2A%28-1%29
4x+=+1%2F4
Divide both sides by 4 (or multiply both sides by 1/4):
x+=+1%2F16