2, 7, 28, 63, 126, ….

Options

A. 210
B. 213
C. 215
D. 219

Explanation

To find the next number in the series 2, 7, 28, 63, 126, we can observe the pattern in the numbers given.

1. **Identify the pattern**:
- The first number is 2, which can be expressed as \(1^3 + 1\).
- The second number is 7, which can be expressed as \(2^3 - 1\).
- The third number is 28, which can be expressed as \(3^3 + 1\).
- The fourth number is 63, which can be expressed as \(4^3 - 1\).
- The fifth number is 126, which can be expressed as \(5^3 + 1\).

2. **Determine the next term**:
- Following the identified pattern, the next term should be based on \(6^3\).
- Since the previous number (126) was derived from \(5^3 + 1\), the next number will be derived from \(6^3 - 1\).
- Calculate \(6^3\):
\[ 6^3 = 216 \]
- Now, subtract 1 from 216:
\[ 216 - 1 = 215 \]

3. **Conclusion**:
- Therefore, the next number in the series is **215**.