In this fraction and number series question, find the odd term out from the series: 1/2, 1, 3/2, 6, 5/2, 3.

Introduction / Context:
This question provides a mixed sequence of fractions and whole numbers: 1/2, 1, 3/2, 6, 5/2, 3. You are asked to identify the odd term out. The series is primarily built from half steps, and one number clearly breaks this structure.

Given Data / Assumptions:

• Series: 1/2, 1, 3/2, 6, 5/2, 3
• The majority of terms follow a simple fractional step pattern.
• Exactly one term does not fit that pattern.

Concept / Approach:
Express each term as a multiple of 1/2. Many fraction sequences are built from regular increments of 1/2 or another simple fraction. If we write all terms with a common denominator, it becomes easier to see which one is out of place.

Step-by-Step Solution:
Step 1: Express each term as a multiple of 1/2.1/2 = 0.5 = 1 * (1/2).1 = 2 * (1/2).3/2 = 1.5 = 3 * (1/2).6 = 12 * (1/2).5/2 = 2.5 = 5 * (1/2).3 = 6 * (1/2).Step 2: Look at the multiples: 1, 2, 3, 12, 5, 6.Step 3: Notice the pattern of small adjacent multiples except one very large jump.The set 1, 2, 3, 5, 6 are reasonably close, while 12 is much larger and does not fit a simple incremental pattern.Step 4: The term corresponding to 12 * (1/2) is 6, which therefore stands out as the odd one.

Verification / Alternative check:
You can also observe that except for 6, all other terms can be seen as part of a natural progression of halves: 1/2, 1, 3/2, 2, 5/2, 3, and so on. The sequence 1/2, 1, 3/2, 5/2, 3 would be a neat steady increase by 1/2 or 1. The sudden jump to 6 breaks the smooth progression, making it the natural odd term.

Why Other Options Are Wrong:
1: Fits perfectly between 1/2 and 3/2 as a multiple of 1/2.
5/2: Continues the smooth increase in halves after 3/2.
3/2: Part of the steady fractional growth from 1/2 and 1 to larger values.

Common Pitfalls:
Many learners treat 6 and 3 as normal since they are clean integers, but the core structure of the series is based on the unit step of 1/2. Failing to convert everything to a common fractional basis can hide this pattern. Always rewrite mixed sequences into a common denominator to reveal the underlying logic.

Final Answer:
The odd term out in the series is 6.