1, 4, 27, 16, ?, 36, 343

Options

A. 25
B. 87
C. 120
D. 125

Explanation

To solve the sequence: 1, 4, 27, 16, ?, 36, 343, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the Pattern**:
The series alternates between cubes of odd numbers and squares of even numbers.
- The first term is \(1\) (which is \(1^3\)).
- The second term is \(4\) (which is \(2^2\)).
- The third term is \(27\) (which is \(3^3\)).
- The fourth term is \(16\) (which is \(4^2\)).
- The fifth term is unknown (denoted as ?).
- The sixth term is \(36\) (which is \(6^2\)).
- The seventh term is \(343\) (which is \(7^3\)).

2. **Determine the Missing Term**:
Following the established pattern:
- The odd-numbered terms are cubes: \(1^3, 3^3, 5^3, 7^3\).
- The even-numbered terms are squares: \(2^2, 4^2, 6^2\).
- The missing term corresponds to the cube of the next odd number, which is \(5\).

3. **Calculate the Cube of 5**:
\[ 5^3 = 5 \times 5 \times 5 = 125 \]

4. **Conclusion**:
The missing term in the sequence is \(125\).

### Final Answer:
The answer is \(125\).

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