1, 14, 31, 64, 133, 264

Options

A. 14
B. 31
C. 264
D. 133

Explanation

To find the odd one out from the series: 1, 14, 31, 64, 133, 264, we will analyze the differences between the consecutive terms to identify any patterns.

### Step-by-step Solution:

1. **Identify the series**: The given series is:
\[ 1, 14, 31, 64, 133, 264 \]

2. **Calculate the first differences**: We will find the differences between consecutive terms:
- \(14 - 1 = 13\)
- \(31 - 14 = 17\)
- \(64 - 31 = 33\)
- \(133 - 64 = 69\)
- \(264 - 133 = 131\)

So, the first differences are:
\[ 13, 17, 33, 69, 131 \]

3. **Calculate the second differences**: Now, we will find the differences between the first differences:
- \(17 - 13 = 4\)
- \(33 - 17 = 16\)
- \(69 - 33 = 36\)
- \(131 - 69 = 62\)

So, the second differences are:
\[ 4, 16, 36, 62 \]

4. **Analyze the second differences**: The second differences do not show a consistent pattern. Let's look at the differences again:
- \(16 - 4 = 12\)
- \(36 - 16 = 20\)
- \(62 - 36 = 26\)

These differences are:
\[ 12, 20, 26 \]

5. **Identify the pattern**: The second differences seem to be increasing but not in a consistent manner. However, if we analyze the differences more closely, we can see that:
- The first differences seem to be multiples of 4, except for the last difference (131).

6. **Check the last difference**: The last first difference (131) is not a multiple of 4. The previous differences (13, 17, 33, 69) can be analyzed further:
- If we consider 64 instead of 62, we can check the pattern again:
- If we replace 264 with 266, we can recalculate:
- \(133 + 64 = 197\)
- \(197 + 69 = 266\)

7. **Conclusion**: The odd one out in the series is 264, as it disrupts the pattern of differences. The correct number should be 266.

### Final Answer:
The odd one out is **264**.