7. The first term of an arithmetic sequence is $a_{1}=7$. For the terms of the sequence, the following holds:

(20) $a_{n}-a_{n-1}=2 n+5, n \geq 2$. What is $a_{100}$?
Solution. Let's expand:

$$
\begin{aligned}
a_{1} & =7 \\
a_{2}-a_{1} & =9 \\
a_{3}-a_{2} & =11 \\
a_{4}-a_{3} & =13 \\
& \vdots \\
a_{100}-a_{99} & =205
\end{aligned}
$$

(10 points)

From here, by adding, we get

$$
\begin{aligned}
a_{1}+a_{2}-a_{1}+a_{3}-a_{2}+a_{4}-a_{3}+\ldots+a_{100}-a_{99} & =7+9+11+13+\ldots+205 \\
a_{100} & =\frac{100(7+205)}{2} \\
a_{100} & =10600
\end{aligned}
$$

(10 points)