Find the wrong number in the following number series:

$$2, 3, 8, 31, 154, 924, 6460$$

Question

Find the wrong number in the following number series:

$$2, 3, 8, 31, 154, 924, 6460$$

Accepted Answer

**Solution:**

1. Observe the pattern in the series: $$2, 3, 8, 31, 154, 924, 6460$$

2. Check the relationship between consecutive terms:
   - From 2 to 3: Multiply by 2 and subtract 1: $$2 	imes 2 - 1 = 3$$
   - From 3 to 8: Multiply by 3 and subtract 1: $$3 	imes 3 - 1 = 8$$
   - From 8 to 31: Multiply by 4 and subtract 1: $$8 	imes 4 - 1 = 31$$
   - From 31 to 154: Multiply by 5 and subtract 1: $$31 	imes 5 - 1 = 154$$
   - From 154 to next term: Multiply by 6 and subtract 1: $$154 	imes 6 - 1 = 923$$ (not 924)

3. The given term is 924, but according to the pattern, it should be 923.

4. Verify the next term:
   - From 923 to 6460: Multiply by 7 and subtract 1: $$923 	imes 7 - 1 = 6460$$ which matches the series.

**Answer:** $924$ is the wrong number in the series.

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