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.