1331 2197 4913 6859 ? 24389

Options

A. 12167
B. 13824
C. 9261
D. 15625

Explanation

To find the missing number in the series: 1331, 2197, 4913, 6859, ?, 24389, we can follow these steps:

### Step 1: Identify the pattern in the series
We need to determine if the numbers in the series are related to perfect cubes.

### Step 2: Calculate the cube roots of the given numbers
1. **1331**: The cube root is \(11\) because \(11^3 = 1331\).
2. **2197**: The cube root is \(13\) because \(13^3 = 2197\).
3. **4913**: The cube root is \(17\) because \(17^3 = 4913\).
4. **6859**: The cube root is \(19\) because \(19^3 = 6859\).
5. **24389**: The cube root is \(29\) because \(29^3 = 24389\).

### Step 3: Identify the missing number
From the cube roots calculated, we see the sequence of cube roots is:
- \(11\), \(13\), \(17\), \(19\), ?, \(29\).

The missing cube root should be the next prime number after \(19\), which is \(23\).

### Step 4: Calculate the cube of the missing number
Now we calculate the cube of \(23\):
\[ 23^3 = 23 \times 23 \times 23 = 12167. \]

### Conclusion
The missing number in the series is **12167**.

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