In the sequence 6, 3, 3, 4.5, 10, which one number is the odd one out if the intended pattern is to repeatedly halve the first term and then multiply by 1, then by 1.5, and so on?

Introduction / Context:
This question presents a short sequence of numbers: 6, 3, 3, 4.5, 10. You are asked to identify the odd one out. The sequence involves both whole numbers and decimals, so it is natural to consider operations such as halving and multiplying by fractional factors. The aim is to find a smooth pattern that all but one term follow.

Given Data / Assumptions:
The sequence is:

• 6
• 3
• 3
• 4.5
• 10

We assume that the first four numbers follow a simple and consistent pattern, and that the last number may have been misgenerated relative to that pattern.

Concept / Approach:
Start by examining how each term might be obtained from the previous one. The initial terms suggest a halving followed by a multiplication, for example 6 to 3 can be seen as halving, and 3 to 3 as multiplication by 1. Continuing this idea with a gradually increasing multiplier leads to a clear expectation for the fifth term. The term that fails this expectation will be the odd one out.

Step-by-Step Solution:
Step 1: From 6 to 3: 6 / 2 = 3, so the second term is half of the first.Step 2: From 3 to 3: 3 * 1 = 3, so the third term is the second term multiplied by 1.Step 3: From 3 to 4.5: 3 * 1.5 = 4.5, so the fourth term is the third term multiplied by 1.5.Step 4: Following this pattern, the next multiplier should reasonably be 2 (an increase of 0.5 again), giving 4.5 * 2 = 9.Step 5: However, the given fifth term is 10, not 9, which suggests that 10 does not fit the smooth pattern of halving and then multiplying by 1, 1.5, 2, and so on.

Verification / Alternative check:
We can summarise the intended pattern as: start at 6, then half it to get 3, then multiply by 1 to stay at 3, then multiply by 1.5 to get 4.5, and finally multiply by 2 to get 9. This yields the consistent sequence 6, 3, 3, 4.5, 9. Comparing this with the given sequence 6, 3, 3, 4.5, 10 shows that only the last term deviates from the expected continuation.

Why Other Options Are Wrong:
The values 6, 3 and 4.5 all follow naturally from the rule described above. Removing any of them would break the halving and then gradually increasing multiplier pattern. Only 10 fails to fit into this structure, since the correct term should have been 9 according to the identified rule.

Common Pitfalls:
Students sometimes attempt to force a single arithmetic or geometric progression on all terms, which can be misleading when the sequence is built from stepwise changes in the operation. Recognising that the sequence uses both division and multiplication by incremental factors makes the logic much clearer.

Final Answer:
The number that does not fit the established pattern is 10.