1. (5 points) Find the value of the function $f(x)$ at the point $x_{0}=4000$, if $f(0)=1$ and for any $x$ the equality $f(x+2)=f(x)+3 x+2$ holds.
Answer: 11998001

Solution: In the equation $f(x+2)-f(x)=3 x+2$, we will substitute for $x$ the numbers $0,2,4, \ldots, 3998$. We get:

$$
\begin{aligned}
& f(2)-f(0)=3 \cdot 0+2 \\
& f(4)-f(2)=3 \cdot 2+2
\end{aligned}
$$

$$
f(4000)-f(3998)=3 \cdot 3998+2
$$

Adding the equations, we get: $f(4000)-f(0)=3 \cdot(0+2+4+\cdots+3998)+2 \cdot 2000=$ $3 \cdot \frac{3998 \cdot 2000}{2}+4000=11998000$. Then $f(4000)=11998001$.