In the following series, find the missing term: 24, 60, 120, 210, ?

Introduction / Context:
This number series problem is based on products of consecutive integers. Many reasoning questions build a sequence from triangular, factorial, or related combinations of integers. Recognising when numbers are products of three consecutive integers is a useful skill for such problems.

Given Data / Assumptions:

• Series: 24, 60, 120, 210, ?
• Exactly one next term must be found.
• The pattern appears to be multiplicative, not just additive.

Concept / Approach:
When numbers increase quickly and do not fit simple addition or multiplication by a single constant, check whether each term can be factorised into a product of small consecutive integers. Product patterns are common because they link nicely to combinatorial or geometric interpretations, and they grow at a moderate but accelerating rate.

Step-by-Step Solution:
Step 1: Factorise 24. We get 24 = 2 × 3 × 4. Step 2: Factorise 60. We see 60 = 3 × 4 × 5. Step 3: Factorise 120. We have 120 = 4 × 5 × 6. Step 4: Factorise 210. We obtain 210 = 5 × 6 × 7. Step 5: The pattern is clear: each term is the product of three consecutive natural numbers, starting from 2 × 3 × 4, then moving the window forward by 1 each time. Step 6: The next natural extension is 6 × 7 × 8. Step 7: Compute 6 × 7 × 8 = 42 × 8 = 336.

Verification / Alternative check:
Writing the terms explicitly as products: 24 = 2×3×4, 60 = 3×4×5, 120 = 4×5×6, 210 = 5×6×7, 336 = 6×7×8. The sliding window of three consecutive integers moves forward by one each time, confirming that 336 is the unique consistent continuation. No other candidate produces such a simple and elegant pattern.

Why Other Options Are Wrong:
Values like 330, 300, or 370 do not factor neatly into the pattern of three consecutive integers continuing from 5, 6, 7. Even if they can be factorised, the integer triplets would either not be consecutive or not follow directly after 5, 6, 7. Therefore these options would break the underlying rule of the series.

Common Pitfalls:
Candidates often begin by checking differences (36, 60, 90, ...) and may get lost in trying to fit an additional pattern on those differences. While such an approach can sometimes work, here the factorisation route is much more direct. Always consider factor patterns when numbers are moderately large and do not fit simple arithmetic progressions.

Final Answer:
The next term in the series, continuing the product of three consecutive integers, is 336.