Question

Which one of the given options is a possible value of \( X \) in the following sequence? \[ 3, 7, 15, X, 63, 127, 255 \]

• A. 35
• B. 40
• C. 45
• D. 31

Hint:

When analyzing a sequence, check for patterns such as differences, ratios, or powers. In this case, each term is one less than a power of 2.

Answer 1

The Correct Option is D

Step 1: Analyze the given sequence. The given sequence is \( 3, 7, 15, X, 63, 127, 255 \). Each number appears to follow a pattern. Observe that each term is one less than a power of 2. Step 2: Express each term. \[ 3 = 2^2 - 1, \quad 7 = 2^3 - 1, \quad 15 = 2^4 - 1, \quad X = 2^5 - 1 = 31. \] The subsequent terms follow the same pattern: \( 63 = 2^6 - 1 \), \( 127 = 2^7 - 1 \), \( 255 = 2^8 - 1 \). Step 3: Conclusion. The missing term \( X = 31 \).