Question

Given that a sequence has a1=3
and r=0.2
, find the third term of the sequence. Then decide which statement is true regarding the sequence.

Option #1: arithmetic sequence

Option #2: geometric sequence

Option #3: another type of sequence

(1 point)
The third term of the sequence is

Answer 1

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**.