1, 4, 27, 16, 125, 36, ….

Options

A. 343
B. 64
C. 121
D. 216

Explanation

To find the next number in the series: 1, 4, 27, 16, 125, 36, …, we can analyze the pattern of the numbers given.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- The series alternates between perfect squares and perfect cubes.
- The first number is \(1\) which is \(1^3\) (cube).
- The second number is \(4\) which is \(2^2\) (square).
- The third number is \(27\) which is \(3^3\) (cube).
- The fourth number is \(16\) which is \(4^2\) (square).
- The fifth number is \(125\) which is \(5^3\) (cube).
- The sixth number is \(36\) which is \(6^2\) (square).

2. **Determine the Next Number**:
- Following the established pattern, the next number should be the cube of the next integer after 6, which is \(7\).
- Calculate \(7^3\):
\[ 7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343 \]

3. **Conclusion**:
- Therefore, the next number in the series is \(343\).

### Final Answer:
The next number in the series is **343**.

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