In each of these questions a number series is given. In each series only one…

Concept

In a difference-pattern number series, you do not look at the terms themselves but at the gaps (first differences) between consecutive terms. When those gaps do not grow by a constant amount, examine the second differences — how each gap changes from the previous gap. The wrong term is the one that forces a single break in an otherwise regular second-difference pattern.

Application

Write the first differences of 210, 228, 250, 274, 302, 332, 365:

1. 228 - 210 = 18

2. 250 - 228 = 22

3. 274 - 250 = 24

4. 302 - 274 = 28

5. 332 - 302 = 30

6. 365 - 332 = 33

Now look at how each gap grows over the previous gap (the second differences): 22-18 = +4, 24-22 = +2, 28-24 = +4, 30-28 = +2. The gaps increase by a steady alternating step of +4, +2, +4, +2, ... So the next increase must again be +4, which means the sixth gap should be 30 + 4 = 34, not 33.

With a gap of 34, the final term must be 332 + 34 = 366. The series prints 365, which makes the last gap only 33 and breaks the +4 / +2 alternation.

Cross-check

Rebuild the full series using the gaps 18, 22, 24, 28, 30, 34: 210, 228, 250, 274, 302, 332, 366. Every second difference is now exactly +4, +2, +4, +2, +4 with no exception, confirming that the printed 365 is the lone wrong number and the intended value is 366.