1,8,27,64,124,216,343

Options

A. 8
B. 27
C. 64
D. 124

Answer

To determine the odd number in the series 1, 8, 27, 64, 124, 216, 343, we can analyze the pattern of the numbers provided.

### Step-by-Step Solution:

1. **Identify the Pattern**:
The first step is to identify if the numbers in the series are perfect cubes. We can check the cubes of the first few integers:
- \(1^3 = 1\)
- \(2^3 = 8\)
- \(3^3 = 27\)
- \(4^3 = 64\)
- \(5^3 = 125\)
- \(6^3 = 216\)
- \(7^3 = 343\)

2. **List the Perfect Cubes**:
From our calculations, we see that:
- 1 (which is \(1^3\))
- 8 (which is \(2^3\))
- 27 (which is \(3^3\))
- 64 (which is \(4^3\))
- 125 (which is \(5^3\)) **(not in the series)**
- 216 (which is \(6^3\))
- 343 (which is \(7^3\))

3. **Compare with the Given Series**:
Now, let's compare the perfect cubes with the numbers in the series:
- The series has: 1, 8, 27, 64, **124**, 216, 343
- The perfect cubes are: 1, 8, 27, 64, **125**, 216, 343

4. **Identify the Odd Number**:
We can see that all numbers in the series are perfect cubes except for 124. The fifth term in the sequence should be 125 (which is \(5^3\)), but instead, we have 124.

5. **Conclusion**:
Therefore, the odd number in the series is **124**.

### Final Answer:
The odd number in the series is **124**.

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