Identify the wrong number in the series:

$$210, 228, 250, 274, 302, 332, 365$$

Question

Identify the wrong number in the series:

$$210, 228, 250, 274, 302, 332, 365$$

Accepted Answer

**Solution:**

1. Observe the differences between consecutive terms:
   - $228 - 210 = 18$
   - $250 - 228 = 22$
   - $274 - 250 = 24$
   - $302 - 274 = 28$
   - $332 - 302 = 30$
   - $365 - 332 = 33$

2. The differences are: $18, 22, 24, 28, 30, 33$

3. Ideally, the differences should follow a pattern. Let's check if the differences increase by a consistent pattern:
   - $22 - 18 = 4$
   - $24 - 22 = 2$
   - $28 - 24 = 4$
   - $30 - 28 = 2$
   - $33 - 30 = 3$

4. The increments alternate between $4$ and $2$, but the last increment is $3$, which breaks the pattern.

5. If the last difference were $32$ instead of $33$, the pattern would be consistent:
   - $18, 22, 24, 28, 30, 32$
   - Differences between differences: $4, 2, 4, 2, 2$

6. Therefore, the last term should be:
   $$332 + 32 = 364$$

7. Since the last term given is $365$, it is incorrect.

**Answer:** $365$

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