27 125 ? 729 1331 2197 3375

Options

A. 612
B. 347
C. 216
D. 343

Explanation

To find the missing number in the series: 27, 125, ?, 729, 1331, 2197, 3375, we will analyze the numbers to identify a pattern.

### Step-by-Step Solution:

1. **Identify the Numbers**: The given series is 27, 125, ?, 729, 1331, 2197, 3375.

2. **Find the Cube Roots**: Let's find the cube roots of the known numbers in the series:
- The cube root of 27 is \(3\) (since \(3^3 = 27\)).
- The cube root of 125 is \(5\) (since \(5^3 = 125\)).
- The cube root of 729 is \(9\) (since \(9^3 = 729\)).
- The cube root of 1331 is \(11\) (since \(11^3 = 1331\)).
- The cube root of 2197 is \(13\) (since \(13^3 = 2197\)).
- The cube root of 3375 is \(15\) (since \(15^3 = 3375\)).

3. **List the Cube Roots**: Now we have the cube roots:
- \(3, 5, ?, 9, 11, 13, 15\)

4. **Identify the Pattern**: The cube roots are odd numbers. The sequence of odd numbers is:
- \(3, 5, 7, 9, 11, 13, 15\)

5. **Determine the Missing Number**: The missing number in the sequence of cube roots is \(7\).

6. **Calculate the Missing Cube**: Now, we find the cube of \(7\):
- \(7^3 = 343\).

7. **Conclusion**: The missing number in the series is \(343\).

### Final Answer:
The missing number is **343**.