Roman-numeral series – fill in the missing term. Sequence: XXIV, XX, __, XII, VIII, …

Introduction / Context:
Here the terms are Roman numerals. Convert each to its Arabic value, detect the numeric pattern, find the missing Arabic number, and convert back to Roman numerals.

Given Data / Assumptions:

• XXIV = 24, XX = 20, __, XII = 12, VIII = 8
• The visible change from 24 to 20 is −4; from 12 to 8 is also −4.
• Assume constant step subtraction by 4.

Concept / Approach:

If the step size is constant (−4), the sequence in Arabic is 24, 20, 16, 12, 8, … Therefore the missing term is 16 in Arabic, which is XVI in Roman numerals.

Step-by-Step Solution:

Verification / Alternative check:

The series in Arabic numerals is a clean arithmetic progression with common difference −4. Re-conversion yields XVI, which fits perfectly between XX and XII.

Why Other Options Are Wrong:

XXII (22) and XIII (13) break the constant −4 rule. IV (4) is far too small. Only XVI keeps the arithmetic progression intact.

Common Pitfalls:

Misreading Roman numerals (e.g., mixing up IV/VI, IX/XI). Convert to Arabic to avoid symbol confusion and apply standard arithmetic checks.

Final Answer:

XVI