To find the second term $a_2$ of the geometric sequence, we use the given recursive formula:

$a_n = \frac{2}{5} a_{n-1}$

where the first term $a_1 = 5$.

Step-by-Step Solution:

1. Substitute $n = 2$ in the recursive formula to find $a_2$: $a_2 = \frac{2}{5} a_1$

2. Substitute $a_1 = 5$: $a_2 = \frac{2}{5} \times 5$

3. Simplify the expression: $a_2 = 2$

Answer:

The correct answer is: $a_2 = 2$

Would you like further details or have any questions?

Here are five related questions for further practice:

1. What is the third term $a_3$ in this sequence?
2. What is the general formula for the $n$-th term in this geometric sequence?
3. If the common ratio were $\frac{3}{5}$ instead of $\frac{2}{5}$, what would $a_2$ be?
4. How would the sequence change if $a_1$ were a different value, say 10?
5. How can you determine if a sequence is geometric or arithmetic by looking at its terms?

Tip: In a geometric sequence with a recursive formula, multiply each term by the common ratio to find the next term.