What will be the next number in the following series ?
0, 7,26, 63,124, ?

Options

A. 147
B. 199
C. 215
D. 187

Answer

To find the next number in the series 0, 7, 26, 63, 124, we need to identify the pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the Pattern**:
Let's look at the numbers in the series:
- 0
- 7
- 26
- 63
- 124

2. **Express Each Term**:
We can express each term in the series using cubes:
- The first term (0) can be expressed as \(1^3 - 1 = 0\)
- The second term (7) can be expressed as \(2^3 - 1 = 8 - 1 = 7\)
- The third term (26) can be expressed as \(3^3 - 1 = 27 - 1 = 26\)
- The fourth term (63) can be expressed as \(4^3 - 1 = 64 - 1 = 63\)
- The fifth term (124) can be expressed as \(5^3 - 1 = 125 - 1 = 124\)

3. **General Formula**:
From the above, we can see that the \(n\)-th term can be represented as:
\[ n^3 - 1 \]
where \(n\) is the position in the series (1 for the first term, 2 for the second term, etc.).

4. **Calculate the Next Term**:
To find the next term (the 6th term), we use \(n = 6\):
\[ 6^3 - 1 = 216 - 1 = 215 \]

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