1. The problem is to find the pattern or rule governing the sequence: 3, 5, 9, 17, 33. 2. Observe the differences between consecutive terms: $5 - 3 = 2$ $9 - 5 = 4$ $17 - 9 = 8$ $33 - 17 = 16$ 3. The differences are 2, 4, 8, 16, which are powers of 2: $2^1, 2^2, 2^3, 2^4$. 4. This suggests the next difference should be $2^5 = 32$. 5. Therefore, the next term in the sequence is: $$33 + 32 = 65$$ 6. The pattern is that each term after the first is obtained by adding powers of 2 starting from $2^1$. Final answer: The next term in the sequence is $65$.