Identify the incorrect number in the following series:

4, 9, 18, 35, 69, 139, 277

Question

Identify the incorrect number in the following series:

4, 9, 18, 35, 69, 139, 277

Accepted Answer

**Solution:**

1. Let's analyze the pattern in the series: 4, 9, 18, 35, 69, 139, 277.

2. Observe the differences between consecutive terms:
   - 9 - 4 = 5
   - 18 - 9 = 9
   - 35 - 18 = 17
   - 69 - 35 = 34
   - 139 - 69 = 70
   - 277 - 139 = 138

3. The differences are: 5, 9, 17, 34, 70, 138.

4. Check if these differences follow a pattern:
   - 5 × 2 - 1 = 9
   - 9 × 2 - 1 = 17
   - 17 × 2 = 34
   - 34 × 2 + 2 = 70 (slight inconsistency)
   - 70 × 2 - 2 = 138

5. The pattern is inconsistent, so let's try another approach.

6. Check if each term is approximately double the previous term minus 1:
   - 4 × 2 - 1 = 7 (not 9)
   - 9 × 2 - 1 = 17 (not 18)
   - 18 × 2 - 1 = 35 (matches)
   - 35 × 2 - 1 = 69 (matches)
   - 69 × 2 - 1 = 137 (not 139)

7. The term 18 does not fit well in this pattern.

8. If we replace 18 with 17, the series becomes:
   4, 9, 17, 35, 69, 139, 277

9. Now check the pattern:
   - 4 × 2 - 1 = 7 (not 9)
   - 9 × 2 - 1 = 17 (matches)
   - 17 × 2 - 1 = 33 (close to 35)
   - 35 × 2 - 1 = 69 (matches)
   - 69 × 2 - 1 = 137 (close to 139)

10. The closest consistent pattern is that each term is roughly double the previous term minus 1, except for the second term.

**Conclusion:** The number 18 is the incorrect term in the series.

**Answer:** 18

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