Identify the incorrect number in the following series:

$$5, 7, 17, 47, 115, 235, 467$$

Question

Identify the incorrect number in the following series:

$$5, 7, 17, 47, 115, 235, 467$$

Accepted Answer

**Solution:**

1. Let's analyze the pattern by checking the relationship between consecutive terms.

2. Calculate the difference between terms:
   - $7 - 5 = 2$
   - $17 - 7 = 10$
   - $47 - 17 = 30$
   - $115 - 47 = 68$
   - $235 - 115 = 120$
   - $467 - 235 = 232$

3. The differences do not form a simple arithmetic or geometric progression. Let's check if the terms follow a pattern based on multiplication and addition.

4. Check if each term is generated by multiplying the previous term by a number and then adding a constant:
   - $5 	imes 1 + 2 = 7$
   - $7 	imes 2 + 3 = 17$
   - $17 	imes 2 + 13 = 47$ (doesn't fit a simple pattern)

5. Try another approach: Check if the terms roughly double plus a constant:
   - $5 	imes 2 - 3 = 7$
   - $7 	imes 2 + 3 = 17$
   - $17 	imes 2 + 13 = 47$
   - $47 	imes 2 + 21 = 115$
   - $115 	imes 2 + 29 = 259$ (expected next term)

6. The actual next term given is $235$, which does not fit the pattern. It should be $259$.

7. Therefore, $235$ is the wrong number in the series.

**Answer:** $235$

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