Question

Find the missing number in the series: \( 5, 12, 26, 54, 110, \_ \)

Hint:

When a series has a consistent difference pattern, check for an arithmetic or geometric progression.

Answer 1

Step 1: Identifying the pattern in the series.
The numbers are increasing rapidly, so we will check for a pattern based on the difference between consecutive terms:
- \( 12 - 5 = 7 \)
- \( 26 - 12 = 14 \)
- \( 54 - 26 = 28 \)
- \( 110 - 54 = 56 \)
The differences are doubling each time: \( 7, 14, 28, 56 \).
Step 2: Predicting the next difference.
The next difference should be \( 56 \times 2 = 112 \).
Step 3: Adding the difference to the last term.
The next term will be \( 110 + 112 = 224 \).
Step 4: Conclusion.
Thus, the missing number is \( 224 \).