All natural numbers starting from 1 were written consecutively, forming a sequence of digits, as follows.

$$
1234567891011121314151617181920212223 \ldots
$$

What is the digit that appears in the 206788th position?
The numbers with one digit form the first 9 terms of the sequence. The 90 two-digit numbers form the next 180 terms. Then come the 2700 terms corresponding to the three-digit numbers, followed by the 36000 terms corresponding to the four-digit numbers, and finally, the 450000 terms corresponding to the five-digit numbers. Thus, enumerating the terms of the sequence, we get 488889 terms.

![](https://cdn.mathpix.com/cropped/2024_05_01_30c9a294a58a6e4b8190g-086.jpg?height=117&width=1362&top_left_y=958&top_left_x=381)

To write all the terms of 1, 2, 3, and 4 digits, we reach the $38889^{\text{th}}$ position of the sequence. Therefore, the digit at the $206788^{\text{th}}$ position is part of a five-digit number, i.e., it is in the block

$$
\underbrace{a_{38890}, \ldots, a_{488889}}_{5 \text{ digits}}
$$

This block is of the form 10000, 10001,.. 99 999. To see how many five-digit numbers exist from position 38889 to position 206788, we divide this difference by 5. Thus, $206788-38889=167899$ and $167899=5 \times 33579+4$. Therefore, we need 33579 five-digit numbers, plus the first four digits of the $33580^{\text{th}}$ five-digit number, which is 43579, to reach the digit at position 206788.

Since the fourth digit of the number 43579 is 7, the digit we are looking for is 7.