2. Each cell of a $5 \times 5$ square contains a number. The numbers in any row and any column form an arithmetic progression. The numbers in the corners of the square are $1, 25, 17, 81$. What number is in the central cell? Don't forget to justify your answer.

| 1 |  |  |  | 25 |
| :--- | :--- | :--- | :--- | :--- |
|  |  |  |  |  |
|  |  | $x$ |  |  |
|  |  |  |  |  |
| 81 |  |  |  | 17 |
2. Answer: 31. Solution. In any arithmetic progression $a_{5}=a_{1}+4 d, a_{3}=a_{1}+2 d \Rightarrow$ $a_{3}=\left(a_{1}+a_{5}\right) / 2$. Therefore, in the third cell of the first column stands the number 41, in the third cell of the last column stands the number 21, and in the middle cell of the second row (i.e., in the central cell of the table) stands the number 31. Grading criteria. Correct solution - 7 points. Numbers in the middle cells are indicated without any justification - 3 points. In all other cases (including one answer without explanation) - 0 points.