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The given recursive formula for the arithmetic sequence is:

\[
a_n = a_{n-1} + 3 \quad \text{with} \quad a_1 = 2
\]

We need to find the fifth term of the sequence (\(a_5\)).

### Step-by-step solution:

1. The first term \(a_1 = 2\).
2. Using the recursive formula, \(a_2 = a_1 + 3 = 2 + 3 = 5\).
3. For the third term, \(a_3 = a_2 + 3 = 5 + 3 = 8\).
4. For the fourth term, \(a_4 = a_3 + 3 = 8 + 3 = 11\).
5. Finally, the fifth term, \(a_5 = a_4 + 3 = 11 + 3 = 14\).

### Answer:
The fifth term of the sequence is **14**.

Would you like further details or clarifications?

Here are 5 related questions to further explore:
1. What is the general formula for an arithmetic sequence?
2. How do you derive the \(n\)-th term of an arithmetic sequence from a recursive formula?
3. What would be the 10th term of this sequence?
4. How does the recursive formula differ from the explicit formula in arithmetic sequences?
5. How do you calculate the sum of the first \(n\) terms of an arithmetic sequence?

**Tip:** The difference between consecutive terms in an arithmetic sequence is constant, making it easy to calculate future terms using the recursive formula.

The recursive formula for an arithmetic sequence is a_n = a_(n-1) + 3 with a_1 = 2. What is the fifth term of the sequence?

Learn how to find the fifth term of an arithmetic sequence using the recursive formula a_n = a_(n-1) + 3 with the first term a_1 = 2. This solution breaks down the step-by-step process of using recursion to calculate each term in the sequence.

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