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:

To solve sequence problems:
1. Look for arithmetic or geometric patterns, such as multiplication, addition, or subtraction.
2. Verify the pattern by applying it to all known terms.
3. Ensure the pattern holds consistently for subsequent terms.

Answer 1

The Correct Option is D

Step 1: Identify the pattern in the sequence. The given sequence appears to double each number and then subtract 1. Verify this for the known terms: \[ 3 \rightarrow 7 = 2 \times 3 - 1, \quad 7 \rightarrow 15 = 2 \times 7 - 1, \quad 15 \rightarrow x = 2 \times 15 - 1. \] The next term is: \[ x = 2 \times 15 - 1 = 30 - 1 = 31. \] Step 2: Verify the continuation of the pattern. Check the subsequent terms using \(x = 31\): \[ 31 \rightarrow 63 = 2 \times 31 - 1, \quad 63 \rightarrow 127 = 2 \times 63 - 1, \quad 127 \rightarrow 255 = 2 \times 127 - 1. \] The pattern holds, confirming that \(x = 31\).