The next number of the sequence 3,5,9,17, 33 …… is

Options

A. 65
B. 60
C. 50
D. 49

Answer

To find the next number in the sequence 3, 5, 9, 17, 33, we will follow these steps:

### Step 1: Identify the given sequence
The sequence provided is:
3, 5, 9, 17, 33

### Step 2: Calculate the differences between consecutive terms
We will find the difference between each pair of consecutive numbers in the sequence:

- 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:
\( 33 - 17 = 16 \)

Now, we have the differences:
2, 4, 8, 16

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

We can observe that each difference is double the previous difference:
- \( 2 \times 2 = 4 \)
- \( 4 \times 2 = 8 \)
- \( 8 \times 2 = 16 \)

This suggests that the next difference will be:
\( 16 \times 2 = 32 \)

### Step 4: Calculate the next term in the sequence
To find the next number in the original sequence, we add the next difference (32) to the last term (33):
\( 33 + 32 = 65 \)

### Conclusion
The next number in the sequence is **65**.

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