Step-by-Step Analysis of the Sequence

To solve this, we first need to determine what the 2028th digit actually is. We can do this by calculating how many digits are contributed by the 1-digit, 2-digit, and 3-digit numbers.

1. Digits from 1-digit numbers (1-9)

• There are 9 single-digit numbers.
• Total digits = 9 × 1 = 9.
• The 2028th digit is beyond this range.

2. Digits from 2-digit numbers (10-99)

• There are 90 two-digit numbers (99 - 10 + 1).
• Total digits = 90 × 2 = 180.
• Cumulative digits up to the number 99 = 9 + 180 = 189.
• The 2028th digit is still beyond this range.

3. Locating the Digit within the 3-digit numbers

• The 2028th digit must fall within the block of 3-digit numbers.
• Position within this block = 2028 - 189 = 1839th digit.
• Since each number in this block has 3 digits, we can find which number contains this digit by dividing by 3:
• 1839 ÷ 3 = 613.
• Because the division is exact, this means the 1839th digit is the last digit of the 613th three-digit number.

4. Identifying the Digit

• The first 3-digit number is 100.
• The 613th three-digit number is 100 + 613 - 1 = 712.
• The last digit of the number 712 is 2.
• Therefore, the 2028th digit in the sequence is 2.

5. Finding the Closest Number

The question asks for the number in the options that is closest to the 2028th digit, which we found to be 2.

• |7 - 2| = 5
• |9 - 2| = 7
• |4 - 2| = 2
• |1 - 2| = 1

The smallest difference is 1.

Conclusion

The closest number to the 2028th digit (which is 2) is 1.