At first glance, the numbers may seem random:

• 7
• 15
• 31
• 63
• ?

But there’s a simple pattern.

Each number is obtained by doubling the previous number and adding 1:

• $7 \times 2 + 1 = 15$7×2+1=15
• $15 \times 2 + 1 = 31$15×2+1=31
• $31 \times 2 + 1 = 63$31×2+1=63

Now apply the same rule one more time:

• $63 \times 2 + 1 = 127$63×2+1=127

✅ Final Answer: 127

Another way to see the pattern is:

• 7 = $2^3 – 1$23−1
• 15 = $2^4 – 1$24−1
• 31 = $2^5 – 1$25−1
• 63 = $2^6 – 1$26−1
• 127 = 27−12^7 – 127−1

So the missing number is 127.