Question

Select the number that can come in place of the question mark (?) in the following series: $$ 3,\ 7,\ 15,\ 31,\ 63,\ ? $$

• A. 127
• B. 128
• C. 138
• D. 212

Hint:

When given a number series, check for multiplication or addition patterns. Look for repeated mathematical operations applied to each term.

Answer 1

The Correct Option is A

Let's observe the pattern in the given series: \[ \begin{aligned} 3 \times 2 + 1 &= 7 \\ 7 \times 2 + 1 &= 15 \\ 15 \times 2 + 1 &= 31 \\ 31 \times 2 + 1 &= 63 \\ 63 \times 2 + 1 &= 127 \\ \end{aligned} \] Each term is obtained by multiplying the previous term by 2 and then adding 1. So, the next term is: \[ 63 \times 2 + 1 = 126 + 1 = 127 \] Answer: \(\boxed{127}\)