The sum of 3 consecutive even numbers is 42. Find the largest number.

Define x:

Let the smallest number be x

The other 2 numbers are x+2 and x+4

Construct Equation:

Sum of the numbers is 42

⇒x + (x + 2) + (x + 4) = 42

Solve for x:

x + (x + 2) + (x + 4) = 42

Remove brackets:

x + x + 2 + x + 4 = 42

Combine like terms:

3x + 6 = 42

Subtract 6 from both sides:

3x = 36

Divide both sides by 3:

x = 12

Find largest number:

The largest number = x + 4 = 12 + 4 = 16

Answer: The largest number is 16.

Let the smallest number among them is n then next two consecutive even terms are: n+2 and n+4

The sum of numbers is 42, so:

↪n+n+2+n+4=42

↪3n+6=42

↪3n=42-6

↪n=36/3

↪n=12

The largest among these numbers is:

n+4

=12+4

=16↪Answer