If a, 12, 16 and b are in continued proportion, find a and b.

Given, a, 12, 16 and b are in continued proportion.

$\therefore \dfrac{a}{12} = \dfrac{12}{16} = \dfrac{16}{b} \\[1em] \Rightarrow \dfrac{a}{12} = \dfrac{12}{16} \text{ and } \dfrac{12}{16} = \dfrac{16}{b} \\[1em] \Rightarrow a = \dfrac{12}{16} \times 12 \text{ and } b = \dfrac{16}{12} \times 16 \\[1em] \Rightarrow a = \dfrac{144}{16} \text{ and } b = \dfrac{256}{12} \\[1em] \Rightarrow a = 9 \text{ and } b = \dfrac{64}{3}.$

Hence, the value of a = 9 and b = $\dfrac{64}{3}$.