2. Indicate all values of $n$ for which the sum of $n$ consecutive terms of the arithmetic progression $22,19,16, \ldots$, starting from the first, is not less than 52.
Solution: For this arithmetic progression, we have: $a_{1}=22, d=-3$. The inequality $S_{n} \geq 52$ must be satisfied, i.e., $\frac{2 a_{1}+d(n-1)}{2} \cdot n \geq 52$. Substituting $a_{1}$ and $d$ into the inequality, we get

$\frac{44-3(n-1)}{2} \cdot n \geq 52 \Leftrightarrow 47 n-3 n^{2} \geq 104 \Leftrightarrow 3 n^{2}-47 n+104 \leq 0 \Leftrightarrow(n-13)\left(n-\frac{8}{3}\right) \leq 0$.

Since $n$ is a natural number, $n \in\left[2 \frac{2}{3}, 13\right] \cap N$, i.e., $n=3,4,5, \ldots, 13$. Answer: $3,4,5, \ldots, 13$.