What will come in place of the question mark (?) in the following number series?
`1728" "2744" "4096" "5832" "8000" "10684" "?`

Options

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

Answer

To solve the given number series and find the missing term, we need to identify the pattern in the series. The series provided is:

`1728, 2744, 4096, 5832, 8000, 10684, ?`

### Step-by-Step Solution:

1. **Identify the Numbers**:
Let's write down the numbers in the series:
- 1728
- 2744
- 4096
- 5832
- 8000
- 10684

2. **Recognize the Cubes**:
We can check if these numbers are cubes of integers:
- \( 12^3 = 1728 \)
- \( 14^3 = 2744 \)
- \( 16^3 = 4096 \)
- \( 18^3 = 5832 \)
- \( 20^3 = 8000 \)
- \( 22^3 = 10684 \)

3. **Identify the Pattern**:
From the above calculations, we can see that the numbers are cubes of even integers:
- \( 12, 14, 16, 18, 20, 22 \)

The pattern shows that each number is the cube of an even integer, increasing by 2 each time.

4. **Find the Next Integer**:
Continuing the pattern, the next even integer after 22 is 24.

5. **Calculate the Cube of 24**:
Now, we need to find \( 24^3 \):
\[ 24^3 = 24 \times 24 \times 24 \]
First, calculate \( 24 \times 24 = 576 \).
Then, multiply by 24:
\[ 576 \times 24 = 13824 \]
Therefore, \( 24^3 = 13824 \).

6. **Final Answer**:
The next term in the series, which replaces the question mark (?), is **13824**.

### Summary:
The missing term in the series is **13824**.