Question

Which of the following numbers are in continued proportion?

• A. 2, 4, 8
• B. 1, 2, 3
• C. 3, 9, 27
• D. 3, 5, 8

Answer 1

Answer: (A), (C)

3, 9, 27

If three numbers a, b, c are in continued proportion then we have $a:b::b:c$.
Which means $b^2$ = $a\times c$ .
i) a = 2, b = 4, c = 8.
As $4^2$ = $2\times 8$, we can say 2, 4, 8 are in continued proportion.

ii) a = 1, b = 2, c = 3.
As $2^2$ $\ne$ $1\times 3$, we can say 1, 2, 3 are not in continued proportion.

iii) a = 3, b = 9, c = 27.
As $9^2$ = $3\times 81$, we can say 3, 9, 81 are in continued proportion.

iv) a = 3, b = 5, c = 8.
As $5^2$ $\ne$ $3\times 8$, we can say 3, 5, 8 are not in continued proportion.