If a, 12, 16, b are in continued proportion, then find the value of a and b.

It is given that a, 12, 16, b are in continued proportion.

Therefore, we can say:$\frac{\mathrm{a}}{12}$$=$$\frac{12}{16}$$=$$\frac{16}{\mathrm{b}}$ 

or $\mathrm{a}=\frac{12\times 12}{16}$

or $\mathrm{a}=\frac{144}{16}$

$\mathrm{a}= 9$

Also, $\frac{12}{16}$$=$$\frac{16}{\mathrm{b}}$ 

Therefore, $12\times \mathrm{b} = 16 \times 16$

or $\mathrm{b}=\frac{16\times 16}{12}$

or $\mathrm{b}=\frac{256}{12}$ 

$\mathrm{b}=$$\frac{64}{3}$