What is the value of ‘X’ in the sequence 2, 7, 22, 67, 202, X, 1822?

Correct Option (3)

The given sequence follows a specific mathematical pattern where each subsequent term is derived by multiplying the preceding term by 3 and then adding 1. The general rule can be expressed as: Term_n = (Term_n-1 × 3) + 1.

Applying this pattern to the sequence:

• 2 × 3 + 1 = 7
• 7 × 3 + 1 = 22
• 22 × 3 + 1 = 67
• 67 × 3 + 1 = 202
• To find the value of X: 202 × 3 + 1 = 606 + 1 = 607
• To verify the next term in the sequence: 607 × 3 + 1 = 1821 + 1 = 1822

Thus, the value of X is 607.

Incorrect Options:

Options 1 (603), 2 (605), and 4 (608) are incorrect because they do not adhere to the established mathematical progression of the sequence. If any of these values were substituted for X, the pattern of multiplying the preceding term by 3 and adding 1 would be broken, and the subsequent term of 1822 would not be correctly generated.