If the average of three consecutive even numbers is 34, find the largest of these numbers.

36

Let the numbers be x, x + 2, x + 4

So, according to the question:

Average of the 3 consecutive numbers is: \(\frac{\text{x + x + 2 + x + 4} }{3 }\)

34 = \(\frac{\text{3x + 6} }{3 }\)

34 x 3 = 3x + 6

102 = 3x + 6

3x = 96

x = 32

So, the largest of these numbers is x + 4 = 36