The average of the three numbers is 154. The first number is twice the second and the second number is twice the third. The first number is

let the 3 numbers be x,y,z

average of the three numbers is 154.

therefore sum of 3 numbers = $$ 154 \times 3 = 462 $$

that is x + y + z = 462 

first number is twice the second

x = 2y...........(1)

second number is twice the third.

y = 2z............(2)

from (1) $$ y = \frac{x}{2} $$

from (2) $$ z = \frac{y}{2} =\frac{x}{4} $$

according to the question

$$ x + \frac{x}{2} + \frac{x}{4} = 462 $$

solving x = 264