Answer: To find the formula for the given geometric sequence, we need to determine the common ratio, r. We can do this by dividing any term by the previous term. For example:
r = 36/72 = 0.5
r = 18/36 = 0.5
r = 9/18 = 0.5
Since the ratio is the same for all consecutive terms, we know that this is a geometric sequence with a common ratio of 0.5.
Now, to find the formula for a geometric sequence, we can use the general formula:
f(n) = a(r^(n-1))
where f(n) is the nth term, a is the first term, r is the common ratio, and n is the index of the term we want to find.
Substituting the given values, we get:
f(1) = 72
f(2) = 36
f(3) = 18
f(4) = 9
Using these values, we can solve for a and r:
f(1) = a(r^(1-1)) = a
a = 72
f(2) = a(r^(2-1)) = 72r
36 = 72r
r = 0.5
Therefore, the formula for the given geometric sequence is:
f(n) = 72(0.5)^(n-1)
Option C represents the correct formula for the sequence:
f(n) = 72(0.5)^(p-1)
Explanation: