What number is to be added to each of the numbers 4, 7, 14 and 22, so that they become the terms of a proportion?

To solve this problem, we need to understand that in a proportion, the product of the means (middle terms) is equal to the product of the extremes (first and last terms).

Let's denote the number to be added to each term as 'x'.

So, the proportion becomes: (4+x) : (7+x) :: (14+x) : (22+x)

According to the rule of proportion, the product of the means equals the product of the extremes. Therefore, we can set up the following equation:

(4+x) * (22+x) = (7+x) * (14+x)

Solving this equation will give us the value of 'x'.

Let's expand both sides:

88 + 26x + x^2 = 98 + 21x + x^2

By simplifying, we get:

5x = 10

So, x = 10 / 5 = 2

Therefore, the number to be added to each of the numbers 4, 7, 14 and 22 to make them terms of a proportion is 2.