Next number in the number sequence is: 22, 11, 33, 16.5, 49.5, ?

Introduction / Context:
This series alternates between division and multiplication. It is a classic pattern in reasoning exams where one step halves the number and the next step triples it. We need to find the next term after 22, 11, 33, 16.5, 49.5.

Given Data / Assumptions:
- Sequence: 22, 11, 33, 16.5, 49.5, ?- The series alternates between larger and smaller values.- A simple fractional operator such as division by 2 and multiplication by 3 is expected.

Concept / Approach:
Observe the relation between every pair of consecutive terms. The presence of exact halves and clean decimal values such as 16.5 is a strong hint of division by 2. Similarly, jumps like 11 to 33 and 16.5 to 49.5 suggest multiplication by 3. Once we confirm this alternation, we can confidently compute the missing term.

Step-by-Step Solution:
- From 22 to 11: 22 / 2 = 11 (division by 2).- From 11 to 33: 11 * 3 = 33 (multiplication by 3).- From 33 to 16.5: 33 / 2 = 16.5 (division by 2).- From 16.5 to 49.5: 16.5 * 3 = 49.5 (multiplication by 3).- The pattern is: divide by 2, then multiply by 3, and repeat.- After 49.5, the next operation in the cycle is division by 2.- So the next term is 49.5 / 2 = 24.75.

Verification / Alternative check:
- Rewriting with the identified rule: 22 ÷ 2 = 11, 11 × 3 = 33, 33 ÷ 2 = 16.5, 16.5 × 3 = 49.5, 49.5 ÷ 2 = 24.75.- The alternating division and multiplication operations are applied consistently, and 24.75 fits perfectly.

Why Other Options Are Wrong:
- 41, 33.5, 26.75 and 29.75 are not equal to 49.5 divided by 2 and do not preserve the strict divide by 2 then multiply by 3 cycle.- Using any of these values would force a different operation at one of the earlier steps, breaking the neat alternation.

Common Pitfalls:
- Some candidates look only at differences rather than ratios and may fail to notice that the pattern is based on division and multiplication.- Rounding errors with decimals can mislead if 16.5 or 24.75 is not handled carefully.- Forgetting to continue the same cycle of operations and inventing a new rule at the end can lead to wrong answers.

Final Answer:
The series alternates between dividing by 2 and multiplying by 3, so the next term after 49.5 is 49.5 ÷ 2 = 24.75.