Answer:
13.6 ft
Step-by-step explanation:
The geometric sequence of arc lengths can be described by ...
f(n) = a·b^n
We have (n, f(n)) = (3, 20) and (7, 12). Using these values, we can find the common ratio (b):
20 = a·b^3
12 = a·b^7
Then ...
12/20 = (a·b^7)/(a·b^3) = b^4 = 3/5
We want the 6th term, which we can get from the 7th term by multiplying by b^-1.
b^(-1) = (b^4)^(-1/4) = (3/5)^(-1/4) = √(√(5/3)) ≈ 1.13622
Then the 6th swing had an arc length of ...
f(6) = f(7)·b^-1
f(6) = (12 ft)(1.13622) ≈ 13.63 ft ≈ 13.6 ft
