Fill the missing number (?) in the given figure.

26

The correct answer is Option (4) → 26

To find the missing number in the circle, we need to identify the mathematical pattern connecting the numbers: 5, 10, 50, and 122.

The Pattern

The numbers follow a pattern based on the squares of prime numbers incremented by 1 ($n^2 + 1$).

• 1st Number: $2^2 + 1 = 4 + 1 = \mathbf{5}$
• 2nd Number: $3^2 + 1 = 9 + 1 = \mathbf{10}$
• 3rd Number (Missing): The next prime number after 3 is 5.

$5^2 + 1 = 25 + 1 = \mathbf{26}$

• 4th Number: The next prime number after 5 is 7.

$7^2 + 1 = 49 + 1 = \mathbf{50}$

• 5th Number: The next prime number after 7 is 11.

$11^2 + 1 = 121 + 1 = \mathbf{122}$

Conclusion

By following the sequence of prime squares plus one, the missing number is 26.