Understanding the Sequence
To find the missing number in the sequence 5, 13, 25, ?, 61, 85, let's first analyze the pattern.
Identifying Differences
1. Calculate the differences between consecutive numbers:
- 13 - 5 = 8
- 25 - 13 = 12
- ? - 25 = ?
- 61 - ? = ?
- 85 - 61 = 24
2. The differences so far are: 8, 12, ?, ?, 24.
Finding a Pattern in the Differences
1. Observe the differences:
- The difference from 5 to 13 is 8.
- The difference from 13 to 25 is 12.
2. The next difference appears to follow an increasing pattern:
- 8 (from 5 to 13)
- 12 (from 13 to 25)
- The next difference could logically be 16 (adding 4 to the previous difference).
3. Continuing this pattern:
- 8, 12, 16, 20, 24
Calculating the Missing Value
1. If we assume the next difference is 16, then:
- ? = 25 + 16 = 41.
2. Now let's check the next difference:
- If ? is 41, then:
- 61 - 41 = 20 (which fits our pattern).
Conclusion
Thus, the missing number in the sequence is 41. This confirms that option 'E' is correct.
- The differences are maintaining a consistent increment.
- The sequence thus logically leads to the conclusion that the missing number is 41.