3, 5, 9, 17, 33, ?

Options

A. 48
B. 49
C. 63
D. 65

Explanation

To find the missing number in the series 3, 5, 9, 17, 33, ?, we can follow these steps:

### Step 1: Identify the series
The given series is: 3, 5, 9, 17, 33, ?

### Step 2: Calculate the differences between consecutive terms
- Difference between 5 and 3:
\( 5 - 3 = 2 \)

- Difference between 9 and 5:
\( 9 - 5 = 4 \)

- Difference between 17 and 9:
\( 17 - 9 = 8 \)

- Difference between 33 and 17:
\( 33 - 17 = 16 \)

### Step 3: List the differences
The differences we calculated are:
- 2, 4, 8, 16

### Step 4: Identify the pattern in the differences
The differences are:
- 2 (which is \( 2^1 \))
- 4 (which is \( 2^2 \))
- 8 (which is \( 2^3 \))
- 16 (which is \( 2^4 \))

We can see that the differences are powers of 2.

### Step 5: Predict the next difference
Following the pattern of powers of 2, the next difference should be:
- \( 2^5 = 32 \)

### Step 6: Add the next difference to the last term in the series
Now, we add this difference to the last term (33):
- \( 33 + 32 = 65 \)

### Conclusion
Thus, the missing number in the series is **65**.