What x is added to each of 10, 16, 22 and 32, the numbers so obtained in this order are in proportion? What is the mean proportional between the numbers (x + 1) and (3x + 1)?

15

The numbers are x + 10, x + 16, x + 22, x + 32

The numbers are in proportion,

⇒ \(\frac{x + 10}{x + 16}\) = \(\frac{x + 22}{x + 32}\)

⇒ 320 + 10x + 32x = 352 + 38x,

⇒ 4x = 32

⇒ x = 8,

According to the question,

The mean proportion of (x + 1) and (3x + 1) = √(x + 1)(3x + 1)

⇒ √(9 x 25) = 15