4.029. Find the sum of all positive even two-digit numbers that are divisible by 3.
## Solution.

From the condition, we have $a_{1}=12, a_{n}=96, d=12$.

Using formulas (4.4) and (4.5), we get

$$
n=\frac{a_{n}-a_{1}}{d}+1 ; n=\frac{96-12}{6}+1=15, S_{n}=\frac{12+96}{2} \cdot 15=810 \text {. }
$$

Answer: 810.