Mathematics

If x, 6, 18 and y are in continued proportion, find the values of x and y.

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Given,

x, 6, 18 and y are in continued proportion.

We can say that,

x, 6, 18 are in proportion.

$\therefore \dfrac{x}{6} = \dfrac{6}{18} \\[1em] \Rightarrow x = \dfrac{6 \times 6}{18} \\[1em] \Rightarrow x = \dfrac{36}{18} = 2.$

Also,

6, 18 and y are in proportion.

$\therefore \dfrac{6}{18} = \dfrac{18}{y} \\[1em] \Rightarrow y = \dfrac{18 \times 18}{6} \\[1em] \Rightarrow y = \dfrac{324}{6} = 54.$

Hence, x = 2 and y = 54.

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