What is a recursive definition for the sequence 3, 5, 9, 17, 33.....

My answer was adding muliple of numbers, is this correct?

pretty vague definition.

For more precision, try

Tn+1 = 2Tn - 1

Your answer is close, but not quite correct. The sequence you provided does involve adding numbers, but it also follows a specific pattern. Let me explain how to find a recursive definition for this sequence.

To identify a recursive definition, we need to find a rule that expresses each term in the sequence in terms of previous terms. In this case, the pattern is that each term is formed by doubling the previous term and subtracting 1.

Let's break it down step by step:
- The first term is 3.
- The second term is obtained by doubling the previous term (3) and subtracting 1, which gives us 2 * 3 - 1 = 5.
- The third term is obtained by doubling the previous term (5) and subtracting 1, giving us 2 * 5 - 1 = 9.
- The fourth term can be found by doubling the previous term (9) and subtracting 1, yielding 2 * 9 - 1 = 17.
- Continuing the pattern, the fifth term is 2 * 17 - 1 = 33.

By observing this pattern, we can establish a recursive definition for this sequence: Each term (except the first one) is obtained by doubling the previous term and subtracting 1.

To summarize, the recursive definition for the sequence you provided is:
- First term: 3
- For n > 1: aₙ = 2 * aₙ₋₁ - 1, where aₙ represents the nth term of the sequence.