Question

If a, b, c are in continued proportion, then which of the following to follow.

• A. $b^2=ac$
• B. c is the third proportional
• C. $\frac{a}{b}=\frac{c}{b}$
• D. $\frac{a}{b}=\frac{d}{c}$

Answer 1

Answer: (A), (B)

The correct options are
A $b^2=ac$
B c is the third proportional

The three quantities $a,b,c$ are said to be in continued proportion if $a:b::b:c$

$\Rightarrow \frac{a}{b}=\frac{b}{c}$

$\Rightarrow ac=b^2$

$\Rightarrow b^2=ac$

Here, $b$ is called the mean proportional of $a$ and $c$, as square of middle term is equal to the product of 1st term and 3rd term.

Also, if $a:b::b:c$, then $c$ is called the third proportional of $a,b$.

Then (A) and (B) are true options.