In the number series 6, 3, 3, 6, 24, ?, what should be the next term that correctly continues the pattern?

Introduction / Context:
This number series tests your ability to recognize patterns that involve repeated multiplication by changing factors. Instead of simple addition or subtraction, the pattern here is built from successive multipliers that follow a clear rule. Identifying such multiplier sequences is important for handling advanced series questions.

Given Data / Assumptions:

• Given series: 6, 3, 3, 6, 24, ?
• The sequence is assumed to be consistent, with exactly one correct next term.
• Operations between terms may involve multiplication, division or both.

Concept / Approach:
We try to relate each term to the previous term by multiplication or division. From 6 to 3, there is a division by 2. From 3 to 3, there is an effective multiplication by 1. From 3 to 6, there is a multiplication by 2. From 6 to 24, there is a multiplication by 4. We notice that the multipliers follow a pattern: 1 divided by 2, then 1, then 2, then 4. This suggests the next multiplier may be 8, doubling each time after the neutral step.

Step-by-Step Solution:
Step 1: 6 to 3 is 6 * (1 / 2) = 3.Step 2: 3 to 3 is 3 * 1 = 3.Step 3: 3 to 6 is 3 * 2 = 6.Step 4: 6 to 24 is 6 * 4 = 24.Step 5: The multipliers after the first term are therefore 1 / 2, 1, 2, 4. These are successive terms multiplied by 2 after the neutral factor 1.Step 6: Continuing this pattern, the next multiplier should be 8. So the next term is 24 * 8 = 192.

Verification / Alternative check:
We can rewrite the pattern as repeated doubling of the multiplier: 1 / 2, 1, 2, 4, 8. Although the first factor is a division by 2, after that the pattern doubles the multiplier each time: 1 to 2 to 4 to 8. Applying 8 to the term 24 yields 192. None of the other options give a continuation that preserves this neat doubling pattern of multipliers.

Why Other Options Are Wrong:
186, 182 and 194 are close to 192 but they do not correspond to multiplying 24 by a simple power of 2. They would require unnatural fractions as multipliers and break the clean pattern of doubling factors. The option 96 corresponds to multiplying 24 by 4, which repeats a multiplier already used and again breaks the established structure.

Common Pitfalls:
Candidates sometimes try to see only addition or subtraction patterns, which clearly do not work here. Others may only look at absolute differences (3, 0, 3, 18) which give no clear systematic rule. The correct strategy for such sequences is to check both multiplicative and divisive links between terms and look at how the multipliers themselves evolve.

Final Answer:
The next term in the series is 192.