There are four numbers such that average of first two numbers is 1 more than the first number, average of firs

Question

There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers, is

Accepted Answer

Let us assume the four numbers to be a, b, c and d in ascending order. Average of first two numbers is 1 more than the first number ( a + b ) 2 = a + 1 \frac{\left(a+b\right)}{2}=a+1 2 ( a + b ) ​ = a + 1 b − a = 2 b-a=2 b − a = 2 b = a + 2 b=a+2 b = a + 2 Average of first three numbers is 2 more th