What will come in place of the question mark (?) in the following number series?
`529" "841" "961" "1369" "1681" "1849" "?`

Options

A. 2809
B. 2601
C. 3249
D. 2209

Answer

To solve the problem of finding the next term in the series `529, 841, 961, 1369, 1681, 1849, ?`, we will follow these steps:

### Step 1: Identify the given numbers
The numbers in the series are:
- 529
- 841
- 961
- 1369
- 1681
- 1849

### Step 2: Determine the square roots of the numbers
Next, we will calculate the square roots of each number to see if they follow a specific pattern:
- √529 = 23
- √841 = 29
- √961 = 31
- √1369 = 37
- √1681 = 41
- √1849 = 43

### Step 3: Identify the pattern in the square roots
Now, we will look at the square roots we have calculated:
- 23
- 29
- 31
- 37
- 41
- 43

We can see that these numbers are prime numbers.

### Step 4: Find the next prime number
The next prime number after 43 is 47.

### Step 5: Calculate the square of the next prime number
Now, we will find the square of 47:
- 47² = 2209

### Conclusion
Thus, the next term in the series is **2209**.

### Final Answer
The answer is **2209**.

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