In the following series, only one number is incorrect. Identify the wrong number:

$$32, 16, 16, 32, 128, 975, 16384$$

Question

In the following series, only one number is incorrect. Identify the wrong number:

$$32, 16, 16, 32, 128, 975, 16384$$

Accepted Answer

**Solution:**

1. Observe the series: $$32, 16, 16, 32, 128, 975, 16384$$

2. Let's analyze the pattern step-by-step:
   - From $32$ to $16$: division by 2 ($32 \div 2 = 16$)
   - Next number is $16$ again, so it repeats.
   - From $16$ to $32$: multiplication by 2 ($16 	imes 2 = 32$)
   - From $32$ to $128$: multiplication by 4 ($32 	imes 4 = 128$)
   - Next number should follow a logical pattern.

3. Check the jump from $128$ to $975$:
   - $975$ is not a multiple or power related to $128$ in a simple way.

4. Check the last number $16384$:
   - $16384 = 2^{14}$, which suggests powers of 2 are involved.

5. The correct number after $128$ should be $512$ (since $128 	imes 4 = 512$), not $975$.

6. Hence, $975$ is the incorrect number in the series.

**Answer:** $975$

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