Find the missing number in the given series?
3, 11, 27, 59, ?

Options

A. 123
B. 121
C. 134
D. 113

Answer

To find the missing number in the series 3, 11, 27, 59, ?, we will analyze the differences between the numbers.

### Step-by-Step Solution:

1. **Identify the series**: The given series is 3, 11, 27, 59, ?.

2. **Calculate the differences between consecutive terms**:
- Difference between 11 and 3:
\[ 11 - 3 = 8 \]
- Difference between 27 and 11:
\[ 27 - 11 = 16 \]
- Difference between 59 and 27:
\[ 59 - 27 = 32 \]

3. **List the differences**:
- The differences we calculated are: 8, 16, and 32.

4. **Observe the pattern in the differences**:
- The differences are:
- 8 (which is \(2^3\))
- 16 (which is \(2^4\))
- 32 (which is \(2^5\))
- We can see that each difference is double the previous one.

5. **Predict the next difference**:
- Following the pattern, the next difference should be:
\[ 32 \times 2 = 64 \]

6. **Calculate the missing number**:
- To find the missing number, we add this next difference (64) to the last known term (59):
\[ 59 + 64 = 123 \]

7. **Conclusion**:
- Therefore, the missing number in the series is **123**.

### Final Answer:
The missing number is **123**.