A number series is given with one term missing. Choose the correct alternative from the given options that will complete the series. 0.5, 2, 3.5, ?, 6.5

Introduction / Context:
This question focuses on a simple arithmetic progression with decimal values where each term increases by a fixed amount. The learner must identify the common difference and use it to find the missing middle term. Such questions are basic but important for building confidence with decimal arithmetic in series.

Given Data / Assumptions:
- Series: 0.5, 2, 3.5, ?, 6.5. - The fourth term is missing. - The pattern is expected to involve equal increments.

Concept / Approach:
In an arithmetic progression, each term differs from the previous term by a constant amount. By calculating the difference between successive known terms and checking for consistency, the common difference can be discovered. The missing term is then obtained by adding this difference to the preceding term or subtracting it from the following term.

Step-by-Step Solution:
Step 1: Compute the difference between the first and second terms: 2 - 0.5 = 1.5. Step 2: Compute the difference between the second and third terms: 3.5 - 2 = 1.5. Step 3: The common difference is therefore 1.5. Step 4: Use this difference to find the fourth term: 3.5 + 1.5 = 5.0. Step 5: Confirm with the last term: 5.0 + 1.5 = 6.5, which matches the given final term.

Verification / Alternative check:
You can also check by using the first and fifth terms. The total change from 0.5 to 6.5 is 6.0, spread over four equal steps. Each step must then be 6.0 / 4 = 1.5. Using this value to fill in the series yields 0.5, 2.0, 3.5, 5.0, 6.5, which confirms the missing term is 5.

Why Other Options Are Wrong:
- Option 4.5 would give a difference of 1.0 from 3.5, which does not match the 1.5 step seen elsewhere. - Option 4 would give a difference of 0.5 from 3.5 and 2.5 to reach 6.5, breaking the equal-step condition. - Option 6 would skip over one increment size and would not fit the constant difference pattern.

Common Pitfalls:
Some learners average the wrong pair of terms or perform incorrect decimal subtraction. Others forget to verify the pattern against all known terms. Always test the discovered difference both forward and backward through the series to avoid hidden mistakes.

Final Answer:
The missing term in the series is 5, so the correct option is 5.