Given that \( a_1 = 3 \) and \( r = 0.2 \), we can determine the type of sequence and calculate the third term.
Since \( r \) (the common ratio) is given, we can infer that this is a geometric sequence.
In a geometric sequence, each term is found by multiplying the previous term by the common ratio.
The formula for the \( n \)-th term of a geometric sequence is:
\[ a_n = a_1 \cdot r^{(n-1)} \]
Let's find the third term (\( a_3 \)):
\[ a_3 = a_1 \cdot r^{(3-1)} = 3 \cdot (0.2)^{2} \]
Calculating \( (0.2)^{2} \):
\[ (0.2)^{2} = 0.04 \]
Thus,
\[ a_3 = 3 \cdot 0.04 = 0.12 \]
Now, we conclude that the third term of the sequence is \( 0.12 \).
Regarding the type of sequence:
Based on the common ratio \( r \) being applied, we can confirm that the correct option is:
Option #2: geometric sequence.