In the mixed series 11M13, 13Q17, ?, 17V22, 19W23, one alphanumeric term is missing. Which option correctly completes the sequence?

Introduction / Context:
This question involves a structured series where each term combines two numbers and one letter: for example, 11M13. We must identify a consistent rule that connects the numbers and letters, and then use that rule to find the missing middle term between 13Q17 and 17V22. This requires careful attention to both the numeric and alphabetic progressions.

Given Data / Assumptions:

• Known terms: 11M13, 13Q17, ?, 17V22, 19W23.
• Each term has the format: number, letter, number.
• We assume the numeric and letter components follow simple, consistent patterns.
• The missing term must align with both the number and letter rules simultaneously.

Concept / Approach:
We consider two number sequences: the left numbers (11, 13, ?, 17, 19) and the right numbers (13, 17, ?, 22, 23). We also examine the letters M, Q, ?, V, W and relate them to these numbers via their alphabet positions. If we can express the letters in a simple way based on the numbers (for example equal to one of the numbers), this often reveals the intended rule with minimal ambiguity.

Step-by-Step Solution:
Step 1: Analyse the left number sequence: 11, 13, ?, 17, 19. The pattern here is clearly +2 each time: 11 → 13 → 15 → 17 → 19. So the left number in the missing term must be 15. Step 2: Analyse the right number sequence: 13, 17, ?, 22, 23. Compute the differences: 17 - 13 = 4, ? - 17 = ?, 22 - ? = ?, 23 - 22 = 1. Notice that 13, 17, 21, 22, 23 would give differences 4, 4, 1, 1, which is a simple pattern. So the right number in the missing term should be 21. Step 3: Examine the letters: 11M13, 13Q17, ?, 17V22, 19W23. M is the 13th letter, matching the right number 13. Q is the 17th letter, matching the right number 17. V is the 22nd letter, matching the right number 22. W is the 23rd letter, matching the right number 23. Step 4: Recognise the rule: the letter position equals the right-hand number in each term. Step 5: The right-hand number in the missing term is 21, so the letter must be the 21st letter, which is U. Step 6: Hence, the missing term is 15U21.

Verification / Alternative check:
Rewriting the complete series as 11M13, 13Q17, 15U21, 17V22, 19W23 we see: left numbers form an arithmetic progression with common difference 2; right numbers grow as 13, 17, 21, 22, 23; and the letter in each term is exactly the right number's alphabetical position. This triple consistency strongly confirms that 15U21 is the correct term.

Why Other Options Are Wrong:
15R18 and 15S19 use incorrect right numbers and letters. 15T20 uses 20 as the right number and T(20) as the letter, which would maintain the letter rule but break the smooth 13, 17, 21, 22, 23 structure for the right numbers. Among the options, only 15U21 satisfies all parts of the pattern at once.

Common Pitfalls:
Learners may try to relate the letter to an average of the two numbers or to the left number, which creates more complicated or inconsistent patterns. Another error is to guess a term that fits only one side (left or right) while ignoring the other. Always check that both the left and right numbers and the letter are all simultaneously consistent with the inferred rule.

Final Answer:
The term that correctly completes the number and letter pattern is 15U21.