1, 8, 9, ?, 25, 216, 49

Options

A. 60
B. 64
C. 70
D. 75

Explanation

To find the missing number in the series: 1, 8, 9, ?, 25, 216, 49, we will analyze the pattern of the numbers given.

### Step-by-Step Solution:

1. **Identify the Numbers**: The series is 1, 8, 9, ?, 25, 216, 49. We need to find the missing number.

2. **Recognize Patterns**:
- The first number is **1**, which is \(1^2\) (1 squared).
- The second number is **8**, which is \(2^3\) (2 cubed).
- The third number is **9**, which is \(3^2\) (3 squared).
- The fourth number is missing.
- The fifth number is **25**, which is \(5^2\) (5 squared).
- The sixth number is **216**, which is \(6^3\) (6 cubed).
- The seventh number is **49**, which is \(7^2\) (7 squared).

3. **Establish the Pattern**:
- The pattern alternates between squares and cubes:
- \(1^2\) (1)
- \(2^3\) (8)
- \(3^2\) (9)
- **?** (should be \(4^3\))
- \(5^2\) (25)
- \(6^3\) (216)
- \(7^2\) (49)

4. **Calculate the Missing Number**:
- The missing number corresponds to \(4^3\).
- Calculate \(4^3 = 4 \times 4 \times 4 = 64\).

5. **Conclusion**:
- The missing number in the series is **64**.

### Final Answer:
The missing number is **64**.