Answer:
The largest of three numbers is 38.
Explanation:
Given : The sum of three consecutive even integers is 108.
We have to find the largest of three consecutive even integer.
Consecutive integers are integer having a difference of one between each term . example 14 , 15, 16 ..
consecutive even integers are integers having a difference of two between them such that first term is in the form of 2n , where n is integers.
Consider the three consecutive even integers are 2n , 2n + 2 , 2n + 4
Also, given The sum of three consecutive even integers is 108.
that is 2n + 2n + 2 + 2n + 4 = 108
Simplify, we get,
6n + 6 = 108
Subtract 6 both side, we get,
6n = 102
Divide by 6 both side, we get,
n = 17
Thus, numbers are 2n = 2 × 17 = 34
2n + 2 = 34 + 2 = 36
2n + 4 = 34 + 4 = 38
Thus, The sum of three consecutive even integers is 108 then integers are 34, 36, 38 .
Thus, The largest of three numbers is 38.