1. (5 points) Find the value of the function $f(x)$ at the point $x_{0}=2000$, if $f(0)=1$ and for any $x$ the equality $f(x+4)=f(x)+3 x+4$ holds.
Answer: 1499001

Solution: In the equation $f(x+4)-f(x)=3 x+4$, we will substitute for $x$ the numbers $0, 4, 8, \ldots, 1996$. We get:

$$
\begin{aligned}
& f(4)-f(0)=3 \cdot 0+4 \\
& f(8)-f(4)=3 \cdot 4+4
\end{aligned}
$$

$$
f(2000)-f(1996)=3 \cdot 1996+4
$$

Adding the equations, we get: $f(2000)-f(0)=3 \cdot(0+4+8+\cdots+1996)+4 \cdot 500=$ $3 \cdot \frac{1996 \cdot 500}{2}+2000=1499000$. Then $f(2000)=1499001$.