What value will come in place of question mark (?) in the number-series given below?
2197 ? 3375 4096 4913

Options

A. 2524
B. 2455
C. 5832
D. None of these

Answer

To solve the problem of finding the missing number in the series 2197, ?, 3375, 4096, 4913, we can follow these steps:

### Step 1: Identify the pattern in the series
The given numbers appear to be perfect cubes. Let's check if they are indeed cubes of consecutive integers.

### Step 2: Calculate the cube roots of the known numbers
- \( 2197 = 13^3 \)
- \( 3375 = 15^3 \)
- \( 4096 = 16^3 \)
- \( 4913 = 17^3 \)

### Step 3: Determine the missing number
From the calculations, we can see that the numbers correspond to:
- \( 13^3 = 2197 \)
- The missing number corresponds to \( 14^3 \)
- \( 15^3 = 3375 \)

### Step 4: Calculate \( 14^3 \)
Now we need to calculate \( 14^3 \):
\[ 14^3 = 14 \times 14 \times 14 = 196 \times 14 = 2744 \]

### Conclusion
Thus, the missing number in the series is \( 2744 \).

### Final Answer
The value that will come in place of the question mark (?) is **2744**.

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