In the alphanumeric series B2, K12, T72, ...., find the next term that correctly follows the pattern.

Introduction / Context:
This is an alphanumeric series where both the letter part and the number part follow their own patterns. To find the next term, we must treat the letters and numbers separately, identify the rule in each component and then combine the results.

Given Data / Assumptions:

• Series: B2, K12, T72, ?
• Each term consists of one letter followed by a positive integer.
• We assume the rules for the letters and the numbers are consistent throughout the series.

Concept / Approach:
The approach is to first map the letters to their positions in the alphabet and inspect the jumps between them. Separately, we examine how the numeric part changes from one term to the next. After identifying these two rules, we extend both patterns simultaneously to obtain the missing term.

Step-by-Step Solution:
Step 1: Consider the letters: B, K and T. Positions are B=2, K=11, T=20.Step 2: Compute differences: 11 - 2 = 9 and 20 - 11 = 9. The letters move forward by 9 positions each time.Step 3: The next letter is therefore 20 + 9 = 29. Modulo 26, 29 corresponds to 3, which is the letter C.Step 4: Now consider the numbers: 2, 12 and 72.Step 5: Each number is multiplied by 6 to produce the next one: 2 × 6 = 12 and 12 × 6 = 72.Step 6: Continue this rule: 72 × 6 = 432.Step 7: Combine the letter and number parts. The next term is C432.

Verification / Alternative check:
Summarising the pattern, the letter advances by a constant shift of +9 (B → K → T → C), and the number is repeatedly multiplied by 6 (2 → 12 → 72 → 432). This produces a very clean and consistent structure. No other combination of letter and number among the options matches both rules at the same time.

Why Other Options Are Wrong:
Options such as A434, A432, C434 or D432 either have the wrong letter, breaking the +9 letter shift, or have an incorrect number that does not equal 72 × 6. Only C432 respects both the alphabetic and numeric rules simultaneously.

Common Pitfalls:
One common mistake is to search only for patterns in the numeric part and ignore that the letters must also follow a regular progression. Another is to assume the numbers grow by repeated addition rather than multiplication, which does not hold here. Exam questions often combine a simple alphabetic shift with a multiplicative numeric pattern.

Final Answer:
The next term in the alphanumeric series is C432.