Final answer:
To find the values of m and n in a continued proportion with the given numbers, we can use the property of continued proportionality and set up a proportion. Then, we can solve for the values of m and n. The values of m and n are 27 and 243, respectively.
Step-by-step explanation:
To find the values of m and n in a continued proportion with the numbers 3, 9, m, 81, and n, we can use the property of continued proportionality. In a continued proportion, the ratio of any two consecutive terms is the same as the ratio of the next two consecutive terms. We can set up the proportion:
3/9 = m/81 = n/m
By cross-multiplying, we get:
3 * 81 = 9 * m = n * 9
Simplifying, we find that:
m = 27
n = 243
Learn more about continued proportion