A number series is given with one term missing. Choose the correct alternative from the given options that will complete the pattern and identify the missing number in the sequence: 105, 130, 180, 255, ?

Introduction / Context:
This question tests recognition of patterns in a numerical series. The sequence 105, 130, 180, 255, ? looks irregular at first glance, but the logic becomes clear when we focus on how each term changes. Such number series questions are common in banking, SSC, and other competitive exams and check a student's ability to detect consistent numerical operations between terms.

Given Data / Assumptions:

• Series given: 105, 130, 180, 255, ?
• We must find the missing term.
• Options: 345, 365, 355, 335.
• Assume the pattern is consistent throughout the sequence.

Concept / Approach:
The usual approaches for such number series include checking differences between consecutive terms, second level differences, multiplication patterns, or combinations of addition and multiplication. Here, the numbers are increasing and the gaps are also increasing, which suggests an arithmetic pattern with increasing differences. Once we see how the differences grow, the missing term can be found easily.

Step-by-Step Solution:
Step 1: Compute first differences.130 - 105 = 25180 - 130 = 50255 - 180 = 75Step 2: Compare these differences.We have 25, 50, 75 which form an arithmetic progression with common difference 25.Step 3: Extend the pattern of differences.The next difference should be 75 + 25 = 100.Step 4: Add this difference to the last known term.Missing term = 255 + 100 = 355.

Verification / Alternative check:
List the sequence with the found term: 105, 130, 180, 255, 355. The consecutive differences are 25, 50, 75, 100. These differences clearly increase by 25 each time, which is a smooth and consistent pattern. There is no contradiction or sudden jump, so the answer 355 fits the series perfectly.

Why Other Options Are Wrong:
345: Difference from 255 would be 90, which breaks the pattern of differences increasing by 25.365: Difference from 255 would be 110, which also does not follow the expected difference of 100.335: Difference from 255 would be 80, again inconsistent with the step of 25 in the differences.

Common Pitfalls:
Many candidates only check first differences but forget to see whether the differences themselves follow a pattern. Some may try multiplication based patterns or random trial and error, which wastes time. The correct way is to keep the approach systematic: first check differences, then second differences, and only then move to more complex ideas if needed.

Final Answer:
The missing term that continues the pattern of increasing differences by 25 is 355.