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

Correct Answer: (C) 607

The sequence follows the recurrence relation $T_n = 3 T_{n-1} + 1$: $2$$\times$ 3 + 1 = 7, $7$$\times$ 3 + 1 = 22, $22$$\times$ 3 + 1 = 67, $67$$\times$ 3 + 1 = 202. Applying this rule to find $X$: $X = 202$$\times$ 3 + 1 = 606 + 1 = 607. Continuing the pattern confirms $607$$\times$ 3 + 1 = 1822.