The defining characteristic of a geometric sequence is called the common ratio. What this means is that each term is a constant multiple of the previous term.
The common ratio for this sequence is:
64/256=16/64=4/16=r=1/4
The first term, a, is equal to 256
Geometric sequences can always be expressed as:
a(n)=ar^(n-1), a=value of first term, r=common ratio, n=term number
Using the values for a and r found earlier we have:
a(n)=256(1/4)^(n-1) and we wish to know the next three terms, n=5,6,7
256(1/4)^4=1, 256(1/4)^5=1/4, 256(1/4)^6=1/16
So the next three term are 1, 1/4, 1/16
