Task B-4.1. Ana is short of 2900 euros for buying a new car. She has decided to save. In the first month, she set aside 50 euros from her earnings. She will set aside 10 euros more each subsequent month. How long does Ana need to save to gather the required amount?
## Solution.

Monthly savings amounts form an arithmetic sequence with a difference of 10, i.e.,

$$
\begin{aligned}
& a_{1}=50, d=10, S_{n}=2900 \\
& \frac{n}{2}[100+(n-1) \cdot 10]=2900 \\
& n^{2}+9 n-580=0 \\
& n_{1}=-29, n_{2}=20
\end{aligned}
$$

Ana needs to save for 20 months.