Question

Complete the series: \(3, 7, 15, 31, 63, \ldots\)

• A. \(95\)
• B. \(111\)
• C. \(127\)
• D. \(128\)

Hint:

In number series problems, check simple operations such as multiplication, addition, subtraction, or powers between consecutive terms. Recognizing the pattern quickly helps determine the next number.

Answer 1

The Correct Option is C

Concept: Many number series follow a recursive pattern where each term is obtained by performing an operation on the previous term. A common pattern is multiplying the previous term and then adding a constant.

Step 1: Observe the pattern between consecutive terms. \[ 3 \rightarrow 7 \rightarrow 15 \rightarrow 31 \rightarrow 63 \] Check the relation: \[ 3 \times 2 + 1 = 7 \] \[ 7 \times 2 + 1 = 15 \] \[ 15 \times 2 + 1 = 31 \] \[ 31 \times 2 + 1 = 63 \] Thus, the pattern is: \[ a_{n+1} = 2a_n + 1 \]

Step 2: Apply the pattern to find the next term. \[ 63 \times 2 + 1 = 126 + 1 \] \[ = 127 \]