A number series is given with one term missing. Select the correct alternative from the given options that will complete the series: 250, 275, 301, ?

Introduction / Context:
This problem is a standard number series question where the learner must detect a pattern in the changes between successive terms. It focuses on the idea of increasing differences rather than a constant difference. Recognizing such patterns is essential for many quantitative aptitude and competitive exam questions.

Given Data / Assumptions:
Given series: 250, 275, 301, ?We need to find the fourth term.We assume a simple, consistent rule governs the differences between consecutive terms.

Concept / Approach:
When the first attempt to find a constant difference fails, the next natural step is to inspect how the differences themselves change. Many number series problems use differences that increase or decrease by a fixed amount. Here, we calculate the differences between known consecutive terms and then look for a pattern in those differences, which can then be extended to determine the missing term.

Step-by-Step Solution:
Step 1: Compute the difference between the second and first term: 275 - 250 = 25.Step 2: Compute the difference between the third and second term: 301 - 275 = 26.Step 3: Observe that the differences are 25 and 26, which suggests that the next difference may follow as 27, increasing by 1 each time.Step 4: Add this expected difference to the third term: 301 + 27 = 328.Step 5: Thus, the missing term that fits the pattern of increasing differences is 328.

Verification / Alternative check:
We can write the completed series as 250, 275, 301, 328. The sequence of differences is then 25, 26, 27. This forms a simple pattern where each difference increases by 1. This type of difference progression is common in exam questions, and the series remains consistent and smooth, confirming that 328 is the correct term.

Why Other Options Are Wrong:
Option 396 would create a jump of 95 from 301, which does not match the smaller, gradually increasing differences of 25 and 26.Option 395 leads to a difference of 94 from 301, again completely inconsistent with the small incremental pattern.Option 300 would actually decrease from 301, breaking the steadily increasing nature of the sequence and failing to follow any simple difference rule.

Common Pitfalls:
One common mistake is to search for multiplicative patterns when the numbers are relatively close and additive patterns are more appropriate. Another error is to stop after computing the first difference and assume it must be constant, without checking for a secondary pattern such as differences that change by a small fixed amount. Careful observation of both first and second differences is often necessary.

Final Answer:
The missing term that correctly completes the series is 328.