Question

Which of the following numbers are in continued proportion:

• A. $3,6$ and $15$
• B. $15,15$ and $48$
• C. $6,12$ and $24$
• D. $12,18$ and $27$

Answer 1

Answer: (C), (D)

$12,18$ and $27$
$6,12$ and $24$

$\left(a\right)3,6$ and $15$ are said to be continued proportion if

$3:6=6:15$

or $\frac{3}{6}=\frac{6}{15}$

or $3\times 15=6\times 6$

$45\ne 36$

Hence $3,6$ and $15$ are not in continued proportion

$\left(b\right)15,15$ and $48$ are said to be continued proportion if

$15:15=15:48$

or $\frac{15}{15}=\frac{15}{48}$

$1\ne \frac{5}{16}$

Hence $15,15$ and $48$ are not in continued proportion

$\left(c\right)6,12$ and $24$ are said to be continued proportion if

$6:12=12:24$

or $\frac{6}{12}=\frac{12}{24}$

$\frac{1}{2}=\frac{1}{2}$

Hence $6,12$ and $24$ are said to be continued proportion.

$\left(d\right)12,18$ and $27$ are said to be continued proportion if

$12:18=18:27$

or $\frac{12}{18}=\frac{18}{27}$

$\frac{2}{3}=\frac{2}{3}$

Hence $12,18$ and $27$ are said to be continued proportion.