Answer: an = 128 * (1/4)^n
Explanation:
The given sequence is not an arithmetic or geometric sequence, but we can try to find a pattern using algebra. Let's assume that the formula for the nth term is of the form:
an = a * b^n
where a and b are constants to be determined. We can find these constants by using the first two points:
a * b^1 = 32 (when n = 1)
a * b^2 = 8 (when n = 2)
Dividing the second equation by the first, we get:
b^1 = (8/32) / (1/2) = 1/4
Substituting this value of b in the first equation, we get:
a * (1/4)^1 = 32
a = 128
Therefore, the formula for the nth term is:
an = 128 * (1/4)^n
We can check this formula using the other given points:
a2 = 128 * (1/4)^2 = 8
a3 = 128 * (1/4)^3 = 2
a4 = 128 * (1/4)^4 = 0.5
So the formula holds for all the given points.