What should come at the place of question mark? : 31, 63, 127, 255, 511, ?
Sequence Pattern Identification
The question presents a sequence: 31, 63, 127, 255, 511, ?
We need to identify the pattern governing this sequence to find the missing term.
Analyzing the Sequence
Let's examine the relationship between consecutive terms or the structure of each term:
- The first term is 31.
- The second term is 63.
- The third term is 127.
- The fourth term is 255.
- The fifth term is 511.
Finding the Mathematical Pattern
Observe the terms in relation to powers of 2:
- $31 = 32 - 1 = 2^5 - 1$
- $63 = 64 - 1 = 2^6 - 1$
- $127 = 128 - 1 = 2^7 - 1$
- $255 = 256 - 1 = 2^8 - 1$
- $511 = 512 - 1 = 2^9 - 1$
The pattern is $2^n - 1$, where n starts from 5 and increases by 1 for each subsequent term.
Calculating the Missing Term
Following the identified pattern, the next term should correspond to $n=10$.
The calculation is:
$2^{10} - 1 = 1024 - 1 = 1023$
Conclusion
Therefore, the number that should come at the place of the question mark is 1023.
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