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

The correct answer is 607 (Option 607).

To find the value of ‘X’ in the given number sequence, let us analyze the pattern or relationship between consecutive terms in the series: 2, 7, 22, 67, 202, X, 1822.

Let us observe how each term is obtained from the previous term:

1^st term = 2
2^nd term = $2\times 3+1=6+1=7$
3^rd term = $7\times 3+1=21+1=22$
4^th term = $22\times 3+1=66+1=67$
5^th term = $67\times 3+1=201+1=202$

As we can see, the rule for finding the next term in the sequence is to multiply the current term by 3 and then add 1.

Following this rule, we can calculate the value of X (the 6^th term):

$\text{X}=202\times 3+1$

$\text{X}=606+1=607$

To verify our result, let us compute the last term (7^th term) using X = 607:

$607\times 3+1=1821+1=1822$

Since this matches the final term given in the sequence, the pattern is correct and verified.

Therefore, the value of ‘X’ is 607.