Find the wrong number in the following number series:

$$0.5, 2, 1, 4, 32, 512, 16384$$

Question

Find the wrong number in the following number series:

$$0.5, 2, 1, 4, 32, 512, 16384$$

Accepted Answer

**Solution:**

1. Let's analyze the pattern by checking the multiplication factor between consecutive terms:

- From $0.5$ to $2$: supposed to multiply by $1$ (but actually $0.5 	imes 1 = 0.5$, which is incorrect for the next term)
- From $0.5$ to $2$: actually $0.5 	imes 4 = 2$

2. Checking the rest of the series with increasing multiplication factors:

- $0.5 	imes 1 = 0.5$ (does not give $2$)
- $0.5 	imes 4 = 2$ (correct)
- $2 	imes 0.5 = 1$
- $1 	imes 4 = 4$
- $4 	imes 8 = 32$
- $32 	imes 16 = 512$
- $512 	imes 32 = 16384$

3. The multiplication factors appear to be doubling each time after the initial step: $0.5, 4, 0.5, 4, 8, 16, 32$ which is inconsistent.

4. The number $2$ does not fit the pattern logically as the series should be:

$$0.5, 1, 4, 32, 512, 16384$$

where each term is multiplied by an increasing power of 2.

**Answer:** $2$

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