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

The third term of the sequence is . Statement # is true for the sequence.

1 answer

To find the third term of the sequence given \( a_1 = 3 \) and \( r = 0.2 \), we need to identify the type of sequence. Since the common ratio \( r \) is provided, we can infer that it is a geometric sequence.

In a geometric sequence, each term is found by multiplying the previous term by the common ratio \( r \).

Given:

  • \( a_1 = 3 \)
  • \( r = 0.2 \)

The second term \( a_2 \) can be calculated as: \[ a_2 = a_1 \times r = 3 \times 0.2 = 0.6 \]

The third term \( a_3 \) can be calculated as: \[ a_3 = a_2 \times r = 0.6 \times 0.2 = 0.12 \]

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

Regarding the type of sequence, since we identified that it has a multiplicative relationship (each term is multiplied by a constant), it is a geometric sequence.

Therefore, the final answer is: The third term of the sequence is 0.12. Statement #2 is true for the sequence (geometric sequence).