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 identifying patterns in sequences, consider operations that involve simple arithmetic manipulations, such as powers, additions, or subtractions, to see if the sequence fits a recognizable mathematical progression.

Answer 1

The Correct Option is D

The sequence appears to be a progression of numbers where each number is derived from an operation involving powers of 2. Specifically, the sequence follows a pattern of \(2^n - 1\), where \(n\) starts from 2. Step 1: Verify the pattern. \(2^2 - 1 = 3\) \(2^3 - 1 = 7\) \(2^4 - 1 = 15\) Assuming \(x = 2^5 - 1\) \(2^6 - 1 = 63\) \(2^7 - 1 = 127\) \(2^8 - 1 = 255\) Step 2: Calculate the value of \(x\). \[ x = 2^5 - 1 = 32 - 1 = 31 \] Step 3: Confirm the option. The value of \(x\) calculated from the pattern is 31, which is option (D). Conclusion.
The correct value of \(x\) in the sequence is \(31\), which is option \( \mathbf{(D)} \).