256,64,16,4 Next three terms of the geometric sequence

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