What should come in place of the question mark (?) in the following number series based on alternating division? 36, 18, 6, 3, 1, ?

Introduction / Context:
This series features a decreasing pattern where terms are obtained by dividing by different integers in an alternating way. The learner must recognise that the sequence alternates division by 2 and division by 3 to reduce the values. Such patterns are common in reasoning tests to check comfort with division and sequence rules.

Given Data / Assumptions:
- Series: 36, 18, 6, 3, 1, ? - The sixth term is missing. - The terms decrease in a non linear manner.

Concept / Approach:
Calculate the ratio between consecutive terms to see by what factor each term is obtained from the previous one. If the ratios follow a repeating pattern, such as dividing by 2, then by 3, and so on, this pattern can be extended to find the next term. The key is to track the operations rather than only differences.

Step-by-Step Solution:
Step 1: Compute ratios between terms. 18 ÷ 36 = 1 / 2, so the first step is divide by 2. 6 ÷ 18 = 1 / 3, so the second step is divide by 3. 3 ÷ 6 = 1 / 2, so the third step is again divide by 2. 1 ÷ 3 ≈ 1 / 3, so the fourth step is divide by 3. Step 2: The pattern alternates between dividing by 2 and dividing by 3. Step 3: After division by 3, the next step should be division by 2 again. Step 4: Therefore, the missing term is 1 ÷ 2 = 0.5.

Verification / Alternative check:
Reconstruct the operations in order: 36 ÷ 2 = 18, 18 ÷ 3 = 6, 6 ÷ 2 = 3, 3 ÷ 3 = 1, and finally 1 ÷ 2 = 0.5. This confirms that the alternating division pattern is consistent and leads to 0.5 as the next term.

Why Other Options Are Wrong:
- Option 0.25 would correspond to dividing 1 by 4, which does not fit the alternating 2 and 3 pattern. - Option 1.5 would increase the value instead of decreasing it and would ignore the division based structure. - Option 0.75 would require dividing by 4 / 3 rather than by 2, which again breaks the clear rule.

Common Pitfalls:
Learners sometimes focus on differences rather than ratios, which is less helpful in division based patterns. Another pitfall is to miscalculate fractions, especially when dividing by 3, leading to incorrect subsequent steps. Careful computation of each division prevents such errors.

Final Answer:
The missing term is 0.5, so the correct option is 0.5.