3, 10, 27, 4, 16, 64, 5, 25, 125

Options

A. 3
B. 4
C. 10
D. 28

Explanation

To solve the series: 3, 10, 27, 4, 16, 64, 5, 25, 125, we need to identify the pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the Groups**:
The series can be divided into three groups based on the pattern:
- First group: 3, 10, 27
- Second group: 4, 16, 64
- Third group: 5, 25, 125

2. **Analyze the First Group (3, 10, 27)**:
- The first number is 3.
- The second number (10) can be seen as \(3^2 + 1 = 9 + 1 = 10\).
- The third number (27) is \(3^3 = 27\).
- Thus, the pattern for the first group is: \(3, 3^2 + 1, 3^3\).

3. **Analyze the Second Group (4, 16, 64)**:
- The first number is 4.
- The second number (16) is \(4^2 = 16\).
- The third number (64) is \(4^3 = 64\).
- Thus, the pattern for the second group is: \(4, 4^2, 4^3\).

4. **Analyze the Third Group (5, 25, 125)**:
- The first number is 5.
- The second number (25) is \(5^2 = 25\).
- The third number (125) is \(5^3 = 125\).
- Thus, the pattern for the third group is: \(5, 5^2, 5^3\).

5. **Summarize the Patterns**:
- The series follows a pattern where each group consists of a number, its square (plus 1 for the first group), and its cube.
- The complete pattern is:
- First group: \(3, 3^2 + 1, 3^3\)
- Second group: \(4, 4^2, 4^3\)
- Third group: \(5, 5^2, 5^3\)

### Conclusion:
The series follows a clear pattern of numbers, their squares, and their cubes. The odd one out in the first group is the number 10, which deviates from the expected square of 3 (which should be 9).