The problem requires us to fill in the blank with the missing Roman numeral to complete the given sequence: DXCVIII, _____, DXCIX, DCL.

1. Problem Description

The problem requires us to fill in the blank with the missing Roman numeral to complete the given sequence: DXCVIII, _____, DXCIX, DCL.

2. Solution Steps

First, we need to convert the given Roman numerals to decimal numbers to identify the pattern:

DXCVIII = 500 + (100 - 10) + 5 + 1 + 1 + 1 = 500 + 90 + 8 = 598

DXCIX = 500 + (100 - 10) + (10 - 1) = 500 + 90 + 9 = 599

DCL = 500 + 100 + 50 = 650

From the first two Roman numerals, we see that they represent consecutive numbers 598 and

5

9

9. Thus the number that should be in the blank is 598+1=

5

9

9. The third number in the sequence is

5

9

9. We see that 650-599=

5

1. So the difference between numbers is 1 and

5

1. This does not seem correct.

However we see that the numbers are $598, 599, x, 650$.

598 and 599 is a sequence.

After that we have

6

5

0. There might be an error in the sequence.

If the sequence is 598, 599, 600, 650 then the answer to the blank is DC.

Let's verify this answer:

DC = 500 + 100 = 600

So the sequence would be DXCVIII, DXCIX, DC, DCL = 598, 599, 600, 650

3. Final Answer

DC