In the following number series, one term is missing: 132, 156, ?, 210, 240, 272. Choose the number that should replace the question mark so that the series follows a consistent pattern.

Introduction / Context:
This problem is a straightforward number series with one missing term. The series appears to increase smoothly, so the key is to look at the differences between consecutive numbers and identify a regular pattern that explains all the known terms and predicts the missing one.

Given Data / Assumptions:

• Series: 132, 156, ?, 210, 240, 272.
• Exactly one missing term is represented by a question mark.
• We expect the series to be governed by simple arithmetic differences.

Concept / Approach:
When terms increase steadily, the differences between consecutive terms often form another simple series, such as a sequence of even numbers or a pattern where the difference itself increases by a fixed amount. We will calculate the known differences and try to fit them into such a pattern.

Step-by-Step Solution:
1. Let the missing term be denoted by N. 2. The series is 132, 156, N, 210, 240, 272. 3. Compute differences using known terms: 156 - 132 = 24 210 - N = ? 240 - 210 = 30 272 - 240 = 32 4. Observe the pattern in the last two differences: 30 and 32. It suggests that the differences might be consecutive even numbers increasing by 2. 5. Assume the full difference pattern is: 24, 26, 28, 30, 32. 6. Starting from 132 and adding 24: 132 + 24 = 156 (matches second term). 7. Next, add 26: 156 + 26 = 182. So N should be 182. 8. Continue to confirm: 182 + 28 = 210, 210 + 30 = 240, 240 + 32 = 272. Everything fits perfectly.

Verification / Alternative check:
Rebuild the entire sequence with the derived pattern. Start from 132 and add differences 24, 26, 28, 30, 32. 132 + 24 = 156 156 + 26 = 182 182 + 28 = 210 210 + 30 = 240 240 + 32 = 272 Every term matches the series when the missing value is 182, so the pattern is consistent.

Why Other Options Are Wrong:

• 196, 199, 204: Substituting any of these numbers for N destroys the even difference pattern 24, 26, 28, 30, 32. The resulting differences become irregular and do not follow a simple increasing by 2 rule.

Common Pitfalls:
Learners sometimes try to force a constant difference or guess without computing all differences. Another frequent mistake is to only check one or two adjacent differences rather than reconstructing the full series from the first term. Always verify that the same rule explains every step in the sequence, especially for all known terms surrounding the missing value.

Final Answer:
The missing number in the series is 182.