Sequence Pattern Calculation

The given sequence is: 3, 7, 15, X, 63, 127, 255.

We need to identify the pattern governing this sequence to find the value of X.

Observe the relationship between consecutive terms or the terms themselves:

• The first term is 3, which can be expressed as $2^2 - 1$.
• The second term is 7, which can be expressed as $2^3 - 1$.
• The third term is 15, which can be expressed as $2^4 - 1$.

The pattern suggests that the $n$-th term in the sequence follows the formula $2^{(n+1)} - 1$.

Applying this pattern to find X, which is the 4th term:

• Term 4 (X): $2^{(4+1)} - 1 = 2^5 - 1$

Calculate the value:

$X = 2^5 - 1 = 32 - 1 = 31$

To confirm, check the subsequent terms:

• Term 5: $2^6 - 1 = 64 - 1 = 63$ (Matches)
• Term 6: $2^7 - 1 = 128 - 1 = 127$ (Matches)
• Term 7: $2^8 - 1 = 256 - 1 = 255$ (Matches)

The identified pattern $2^{(n+1)} - 1$ consistently applies to the sequence.

Therefore, the possible value of X is 31.