What is the next number in the sequence: 3, 5, 9, 17, 33?

To determine the next number in the sequence 3, 5, 9, 17, 33, it's important to analyze the pattern in the differences between consecutive terms.

Starting from the first number, we look at how each number relates to the previous one:

• From 3 to 5, the difference is 2.

• From 5 to 9, the difference is 4.

• From 9 to 17, the difference is 8.

• From 17 to 33, the difference is 16.

We can see that the differences are 2, 4, 8, and 16. These differences themselves form a pattern where each difference is double the previous one. This is a sequence of powers of 2:

• 2 (which is (2^1))

• 4 (which is (2^2))

• 8 (which is (2^3))

• 16 (which is (2^4))

Continuing this pattern, the next difference should be (2^5), which is 32.

Now, if we add this next difference (32) to the last number in the sequence (33), we get:

33