The fourth proportional to 4, 6, and 8 is m. The third proportional to 8 and m is n. What is the value of n?
18
The fourth proportional to \(4, 6, 8\) satisfies \(4:6 = 8:m\), so \(m = \frac{6 \times 8}{4} = 12\).
The third proportional to \(8\) and \(m = 12\) satisfies \(8:12 = 12:n\).
So \(n = \frac{12 \times 12}{8} = \frac{144}{8} = 18\).
Hence, the value of n is 18.
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