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 can analyze the differences between the consecutive terms.

**Step 1: Write down the sequence.**
The given sequence 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:
\( 33 - 17 = 16 \)

So, the differences are:
2, 4, 8, 16.

**Step 3: Identify the pattern in the differences.**
The differences we calculated are:
2, 4, 8, 16.
These differences are powers of 2:
\( 2^1, 2^2, 2^3, 2^4 \).

**Step 4: Predict the next difference.**
Following the pattern, the next difference should be:
\( 2^5 = 32 \).

**Step 5: Add the next difference to the last term of the sequence.**
To find the next term in the sequence, we add the next difference (32) to the last term (33):
\( 33 + 32 = 65 \).

**Final Answer:**
The next number in the sequence is **65**.

---