Which of the following statements correctly describes the sequence 3, 8, 13, 18, . . .?

Question

Statement #1: It is an arithmetic sequence.

Statement #2: It is a geometric sequence.

(1 point)
Statement #$$ correctly describes the sequence.

Answer 1

To determine which statement correctly describes the sequence 3, 8, 13, 18, ..., let's examine the definitions of arithmetic and geometric sequences.

1. Arithmetic Sequence: A sequence is arithmetic if the difference between consecutive terms is constant.

   • The differences between the terms in this sequence are:
     • 8 - 3 = 5
     • 13 - 8 = 5
     • 18 - 13 = 5
   • Since the difference is constant (5), this is an arithmetic sequence.

2. Geometric Sequence: A sequence is geometric if the ratio between consecutive terms is constant.

   • The ratios between the terms in this sequence are:
     • 8 / 3 ≈ 2.67
     • 13 / 8 = 1.625
     • 18 / 13 ≈ 1.38
   • Since the ratios are not constant, this is not a geometric sequence.

Based on the analysis, we find that Statement #1 accurately describes the sequence as an arithmetic sequence, while Statement #2 does not apply.

Therefore, the correct answer is: Statement #1 correctly describes the sequence.