Insert the missing number in the series: 15, 31, 63, 127, 255, (?)

This is a number-series question governed by a single fixed rule that converts each term into the next one. To find that rule, compare consecutive terms until one operation (or one combination of operations) explains every pair consistently, then apply that same rule once more to the last given term to get the missing value.

1. 15 × 2 + 1 = 31

2. 31 × 2 + 1 = 63

3. 63 × 2 + 1 = 127

4. 127 × 2 + 1 = 255

5. 255 × 2 + 1 = 511

The rule — double the term and add 1 — holds across all four given pairs, so applying it to 255 gives the missing term as 511.

Reversing the last step confirms it: (511 − 1) ÷ 2 = 255, which matches the given term, so the rule has been applied correctly.

Hence, the missing number in the series is 511.