Step 1 : Understanding the Question
This is an alphanumeric series completion problem. It requires the identification of two independent patterns: one for the alphabetical characters and one for the numerical values. To solve this, we must determine the incremental logic used to transition from one term to the next and then apply that logic to find the missing central term in the sequence.
Step 2 : Key Formulas and approach
The approach involves "Splitting the Series." We treat the letters and the numbers as two separate sequences. For the letters, we translate them into their numerical positions in the alphabet (A=1, B=2, etc.) to detect the shift. For the numbers, we look for a constant difference or a specific arithmetic progression.
Key Approach:
1. Alphabet Pattern: Identify the jump (e.g., +1, +2).
2. Number Pattern: Identify the arithmetic difference (e.g., +5).
Step 3 : Detailed Explanation
Analyzing the Alphabet Sequence: The sequence of letters is M, O, (?), S, U. In the English alphabet, M is the $13^{th}$ letter and O is the $15^{th}$ letter. The jump from M to O is $+2$.
Verifying the Alphabet Jump: Following the $+2$ logic, the missing letter would be the $17^{th}$ letter ($15 + 2 = 17$), which is Q. To check this, we look at the next term: $Q(17) + 2 = 19$, which is S, and $S(19) + 2 = 21$, which is U. The pattern is confirmed.
Analyzing the Numerical Sequence: The numbers given are 13, 18, (?), 28, 33. We look for the difference between the known consecutive terms. $18 - 13 = 5$, and $33 - 28 = 5$.
Calculating the Missing Number: Since the common difference is 5, we add it to the second number to find the missing value: $18 + 5 = 23$. We verify this by adding 5 again: $23 + 5 = 28$, which matches the next term.
Combining the Results: By merging the identified letter (Q) and the identified number (23), we obtain the full term: Q23.
Step 4 : Final Answer
The correct next term in the series is Q23, which corresponds to option (B).