jmc

If the arithmetic sequence of three consecutive even integers is $a,a+2,a+4$, we find the sum of the terms by multiplying the average of the first and last term $\frac{a+(a+4)}{2}$ by the number of terms, $3$. This gives us the equation $$\frac{2a+4}{2}\cdot 3=66.$$ Solving for $a$, we find $a=\boxed{20}$.