Answer:
The difference between the largest possible value of the greatest integer and the least possible value of the greatest of the five integers = 4
Step-by-step explanation:
Step 1:-
let 'x' be the number
The sequence of arithmetic progression of distinct positive integers
x , x+1 , x+2 , x+3 , x+4
Given the average of five distinct positive integers is 10
[tex]\frac{x+x+1+x+2+x+3+x+4}{5} = 10[/tex]
on simplification , and cross multiplication , we get
5x +10 = 5 X10
5x +10 =50
subtracting'10' on both sides, we get
5x +10 - 10 = 50 -10
5x =40
dividing '5' on both sides, we get
x = 8
The number is '8'
Step 2:-
Now the arithmetic sequence of five numbers are
x , x+1 , x+2 , x+3 , x+4
8 , 9, 10 , 11 , 12
In this sequence is smallest number is '8' and
The largest number is '12'
the difference between the largest possible value of the greatest integer and the least possible value of the greatest of the five integers
= largest possible value - least possible value
= 12 - 8 =4
Final answer = 4
