What number should be added to each of the number 94 2426 so that the resulting number are in continued proportion?

What number must be added to each of the numbers 16, 26 and 40 so that the resulting numbers may be in continued proportion?

Let x be added to each number then16 + x, 26 + x and 40 + xare in continued proportion.⇒ `(16 + x)/(26 + x) = (26 + x)/(40 + x)`Cross Multiplying(16 + x) (40 + x) = (26 + x) (26 + x)

⇒ 640 + 16x + 40x + x2 = 676 + 26x + 26x + x2

⇒ 640 + 56x + x2 = 676 + 52x + x2
⇒ 56x + x2 - 52x - x2 = 676 - 640⇒ 4x = 36⇒ x = `(36)/(4)` = 9

∴ 9 is to be added.

Concept: Concept of Proportion

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