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What number must be added to each of the numbers 7, 4 and 2 so that the resulting numbers may be in a continued proportion?

What number must be added to each of the numbers 7, 4 and 2 so that the resulting numbers may be in a continued proportion? Correct Answer 2

Given

7,4 and 2 should be in a continued proportion

Concept

Continued proportion means the ratio between the first and the second is equal to the ratio between the second and the third

Calculation

let x is added in each number

(7 + x)/(4 + x) = (4 + x)/(2 + x)

⇒ (7 + x) (2 + x) = (4 + x) (4 + x)

⇒ 14 + 7x + 2x + x2 = 16 + 8x + x2

⇒ 14 + 9x + x2 = 16 + 8x + x2

⇒ 14 + 9x = 16 + 8x

⇒ 9x - 8x = 16 - 14

⇒ x = 2

∴ 2 must be added to each of the numbers 7, 4 and 2 so that the resulting numbers may be in a continued proportion.

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