Check whether the following numbers are in continued proportion.

i. 2, 4, 8 ii. 1, 2, 3

iii. 9, 12, 16 iv. 3, 5, 8

(i) Three numbers ‘a’, ‘b’ and ‘c’ are said to be continued proportion if a, b and c are in proportion,

i.e. a:b∷b:c

or b² = ac

Here, a = 2, b = 4 and c = 8

∴ (4)² = 2 × 8

⇒ 16 = 16, which holds true.

∴ 2, 4, 8 are in continued proportion.

(ii) Three numbers ‘a’, ‘b’ and ‘c’ are said to be continued proportion if a, b and c are in proportion,

i.e. a:b∷b:c

or b² = ac

Here, a = 1, b = 2 and c = 3

∴ (2)² = 1 × 3

⇒ 4 = 3, which does not hold true.

∴ 1, 2, 3 are not in continued proportion.

(iii) Three numbers ‘a’, ‘b’ and ‘c’ are said to be continued proportion if a, b and c are in proportion,

i.e. a:b∷b:c

or b² = ac

Here, a = 9, b = 12 and c = 16

∴ (12)² = 9 × 16

⇒ 144 = 144, which holds true.

∴ 9, 12, 16 are in continued proportion.

(iv) Three numbers ‘a’, ‘b’ and ‘c’ are said to be continued proportion if a, b and c are in proportion,

i.e. a:b∷b:c

or b² = ac

Here, a = 3, b = 5 and c = 8

∴ (5)² = 3 × 8

⇒ 25 = 24, which does not hold true.

∴ 3, 5, 8 are not in continued proportion.