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
. Statement #
is true for the sequence.

Answer 1

Given that the first term \( a_1 = 3 \) and the common ratio \( r = 0.2 \), this defines a geometric sequence.

In a geometric sequence, each term can be found by multiplying the previous term by the common ratio \( r \). The formula for the \( n \)-th term of a geometric sequence is:

\[
a_n = a_1 \cdot r^{(n-1)}
\]

To find the third term \( a_3 \):

\[
a_3 = a_1 \cdot r^{(3-1)} = 3 \cdot 0.2^{2}
\]

Calculating \( 0.2^2 \):

\[
0.2^2 = 0.04
\]

Now substituting this back into the formula for \( a_3 \):

\[
a_3 = 3 \cdot 0.04 = 0.12
\]

Therefore, the third term of the sequence is \( 0.12 \).

Now, let's classify the type of sequence:
- Since the sequence has a common ratio \( r \) (and the common difference is not constant), it is a geometric sequence.

So, to summarize:
The third term of the sequence is **0.12**. Statement **Option #2** is true for the sequence (it is a geometric sequence).