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

Answer:

$4034.40

step-by-step explanation:

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40