What should come in place of the question mark (?) in the following number series, which follows a multiply then subtract pattern? 8, 6, 9, 23, ?

Introduction / Context:
This number series uses a compound pattern where each term is derived from the previous term by multiplying with an increasing integer and then subtracting the next integer. Such series test a higher level of pattern recognition, because both multiplication and subtraction change at each step.

Given Data / Assumptions:
- Series: 8, 6, 9, 23, ? - The fifth term is missing. - The pattern likely involves operations that depend on the term position.

Concept / Approach:
Instead of looking only at simple differences or ratios, consider how each term might be obtained from the previous term using position based operations. One common pattern is of the form: multiply by n and then subtract (n plus 1), where n increases step by step. By checking this idea against the given terms, the exact rule can be identified.

Step-by-Step Solution:
Step 1: Move from 8 to 6: 8 × 1 - 2 = 6. Here the multiplier is 1 and the subtracted value is 2. Step 2: Move from 6 to 9: 6 × 2 - 3 = 12 - 3 = 9. Now the multiplier is 2 and the subtracted value is 3. Step 3: Move from 9 to 23: 9 × 3 - 4 = 27 - 4 = 23. Here the multiplier is 3 and the subtracted value is 4. Step 4: The pattern is therefore: multiply by n and subtract (n plus 1), where n starts at 1 and increases by 1 each time. Step 5: For the next term, n becomes 4, so compute 23 × 4 - 5. Step 6: 23 × 4 = 92, and 92 - 5 = 87.

Verification / Alternative check:
Rebuild the series using this rule from the start. Begin with 8, then 8 × 1 - 2 = 6, 6 × 2 - 3 = 9, 9 × 3 - 4 = 23, and 23 × 4 - 5 = 87. The pattern works consistently at every step, confirming that 87 is the correct next term.

Why Other Options Are Wrong:
- Option 53 does not arise from 23 × 4 - 5 and therefore breaks the established multiply then subtract rule. - Option 75 would require 23 × 4 minus a different number, which is not consistent with subtracting n plus 1. - Option 110 is again inconsistent with the position based operation observed in earlier terms.

Common Pitfalls:
Learners often focus only on differences between terms and may miss patterns where both multiplication and subtraction change with each step. Another pitfall is to guess the next term using approximate growth rather than confirming a precise rule. For advanced series, always test potential rules rigorously against every transition.

Final Answer:
The missing term that follows the pattern is 87, so the correct option is 87.