Q. 43.8( 19 Votes )

# 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

Answer :

(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 b^{2} = 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 b^{2} = 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 b^{2} = 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 b^{2} = 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.

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Check whether the following numbers are in continued proportion.

i. 2, 4, 8

ii. 1, 2, 3

iv. 3, 5, 8MHB - Math Part-I

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i. 37: 500 ii. 5/8

iii. 22/30 iv. 5/16

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i. ii.

iii. iv.

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