A series is given with one term missing. Choose the meaningful number from the given responses that will complete the series: 206, 221, 251, 296, ?, 431

Introduction / Context:
This problem shows a series in which the differences between consecutive terms are multiples of a fixed number. Here the increments appear to grow in a regular way, suggesting that each step adds 15 times a simple sequence of integers. The series is 206, 221, 251, 296, ?, 431, and we must find the missing term that keeps this structure intact.

Given Data / Assumptions:
- Given series: 206, 221, 251, 296, ?, 431.- Only the fifth term is missing.- The values are increasing.- Differences are likely to be multiples of 15 following a simple pattern.

Concept / Approach:
We compute successive differences and then see whether those differences form a simple pattern, such as 15, 30, 45, 60, 75. Once we recognise that pattern, we can add the appropriate difference to find the missing term and confirm that the last step also fits the rule.

Step-by-Step Solution:
- From 206 to 221: 221 - 206 = 15.- From 221 to 251: 251 - 221 = 30.- From 251 to 296: 296 - 251 = 45.- The differences are 15, 30, 45, which are 15 * 1, 15 * 2, 15 * 3.- The next two differences should be 15 * 4 = 60 and 15 * 5 = 75.- Therefore, the missing term after 296 is 296 + 60 = 356.- Check the last term: 356 + 75 = 431, which matches the final value in the series.

Verification / Alternative check:
- With 356 inserted, the full difference sequence becomes 15, 30, 45, 60, 75.- This is an arithmetic progression in the differences with common difference 15.- No other candidate produces such a neat multiple of 15 structure extending to 431.

Why Other Options Are Wrong:
- 326, 311 and 341 lead to differences that are not 60 and 75 at the fourth and fifth steps.- 371 would give a last difference of 60 to reach 431, which does not continue the intended sequence 15, 30, 45, 60, 75.- Only 356 maintains the consistent growth of differences by 15 each time.

Common Pitfalls:
- Focusing only on the main numbers without analysing differences can hide the multiple of 15 pattern.- Miscalculating a single difference, such as confusing 296 - 251, can disturb recognition of the sequence.- Guessing based solely on approximate size, rather than verifying the full pattern, can lead to incorrect options.

Final Answer:
The differences are 15, 30, 45, 60, 75, so the missing term between 296 and 431 is 356.