Consider the sequence with a first term of $256$, followed by $64,16,..$ 

1. Write the next three terms of this sequence, then find an equation for the sequence.

   Hint (a):

   Note that each number is one-fourth of the preceding number.

   Answer (a):

   Next three terms: $4,1,0.25$

   $\text{The equation is } t(n) = 1024(0.25)^{n}.$

2. If you were to keep writing out more and more terms of the sequence, what would happen to the terms?

   Hint (b):

   As you write more terms, do they get smaller or larger? Do they ever become negative?

   Answer (b):

   They get smaller, but never reach zero or become negative.

3. Sketch a graph of the sequence. What happens to the points as you go farther to the right?

   Hint (c):

   Which $y$-value do the numbers approach?

   Answer (c):

   

4. What is the domain of the sequence? What is the domain of the function with the same equation as this sequence?

   Hint (d):

   Which $x$-values are on this graph?