Understanding the Sequence
The given sequence is: 105, 127, 151, ?, 205, 235.
To find the missing number, let's analyze the differences between consecutive terms.
Calculating Differences
- Difference between 127 and 105:
- 127 - 105 = 22
- Difference between 151 and 127:
- 151 - 127 = 24
Now, let's denote the missing number as "x".
- Difference between x and 151:
- x - 151 = ?
- Difference between 205 and x:
- 205 - x = ?
Identifying the Pattern
Looking at the differences we have so far:
- First difference: 22
- Second difference: 24
It appears that the differences are increasing by 2. Therefore, the next difference should be:
- Third difference: 24 + 2 = 26
Now we can find the missing number "x":
- x = 151 + 26
- x = 177
Confirming the Next Difference
Now, let's check the difference between 205 and the newly found "x":
- 205 - 177 = 28
This difference also fits the pattern:
- First difference: 22
- Second difference: 24
- Third difference: 26
- Fourth difference: 28
Conclusion
Hence, the missing number in the sequence is 177, making option 'C' the correct answer. The sequence of differences increases consistently by 2, confirming the pattern throughout the series.