Question

If quantities 3, a, 27, and b are in continued proportion, then the respective values of ‘a’ and ‘b’ are:

[1 Mark]

• A. 3,9
• B. 6,24
• C. 9,27
• D. 9,81

Answer 1

The correct option is D 9,81

Given
3, a, 27, and b are in continued propotion.
$\therefore 3:a::a:27$
$\Rightarrow \frac{3}{a}=\frac{a}{27}=\frac{27}{b}$
$\Rightarrow \frac{3}{a}=\frac{a}{27}\text{and}\frac{a}{27}=\frac{27}{b}$
$\Rightarrow a^2=81\text{and}ab=27\times 27$
$\Rightarrow a=9\text{and}b=\frac{27\times 27}{a}=\frac{27\times 27}{9}=81$