A two letter series is given as JN, OR, UW, BC, ? Based on the pattern in the English alphabet, which pair of letters should come next to continue this sequence correctly?

Introduction / Context:
This alphabet series uses two letter pairs: JN, OR, UW, BC, followed by a missing pair. The pattern involves systematic jumps in the alphabet for both the first and the second letters, and, importantly, the series wraps around from Z back to A. Recognising and extending this pattern is key to identifying the correct next pair.

Given Data / Assumptions:

• Series: JN, OR, UW, BC, ? • Options: KM, JJ, JK, KJ • Alphabet positions: J 10, N 14, O 15, R 18, U 21, W 23, B 2, C 3, K 11, M 13. • Assumption: Both first letters and second letters follow consistent numeric progressions with increasing steps, and the alphabet wraps after Z.

Concept / Approach:
We treat the sequence of first letters J, O, U, B as one sequence and the sequence of second letters N, R, W, C as another. By converting both sequences into numeric positions and analysing the differences between terms, we discover steadily increasing step sizes. Extending these step sizes and applying modular arithmetic for wrap around allows us to compute the positions for the next pair and hence the letters.

Step-by-Step Solution:
Step 1: First letters: J, O, U, B have positions 10, 15, 21, and 2. Step 2: Differences are 15 − 10 = 5, 21 − 15 = 6, and, going forward in a circular alphabet, from 21 to 2 is 7 (since 21 + 7 = 28 and 28 − 26 = 2). Step 3: The first letter steps are therefore +5, +6, +7. The natural next step is +8. Step 4: Apply +8 to the last position 2: 2 + 8 = 10. Position 10 is J. So the next first letter is J. Step 5: Second letters: N, R, W, C have positions 14, 18, 23, and 3. Step 6: Differences are 18 − 14 = 4, 23 − 18 = 5, and, going forward circularly, from 23 to 3 is 6 (since 23 + 6 = 29 and 29 − 26 = 3). Step 7: So the second letter steps are +4, +5, +6. The next step should be +7. Step 8: Apply +7 to the last position 3: 3 + 7 = 10, which is J again. Step 9: Therefore both first and second letters for the next pair are J, and the required pair is JJ.

Verification / Alternative check:
We can list the first letter positions as 10, 15, 21, 2, 10 and the second letter positions as 14, 18, 23, 3, 10. Each sequence shows increasing step sizes of 5, 6, 7, 8 for the first letters and 4, 5, 6, 7 for the second letters when computed with wrap around. Plugging in the computed value 10 for both positions yields letter J for each, giving JJ. Checking the options shows that only JJ satisfies these derived positions.

Why Other Options Are Wrong:
KM, JK, and KJ all break at least one of the column wise numeric patterns when converted to positions, producing step sizes that are not the correct next numbers in the difference sequences.

Common Pitfalls:
Students may overlook the wrap around from Z to A and simply subtract positions, which can give misleading differences. Another pitfall is to assume a constant step rather than noticing that the step size itself is increasing by one. Carefully using modular arithmetic for an alphabet treated as circular and observing the pattern of differences helps avoid these issues.

Final Answer:
The pair of letters that correctly continues the series JN, OR, UW, BC is JJ.