Question

6.6 comparing linear and exponential functions (sequences) quiz

which sequence is arithmetic?

2, 6, 18, 54
5, 9, 13, 17
3, 9, 27, 81
4, 8, 16, 32

Explanation:

Define arithmetic sequence

Using the Arithmetic Sequences knowledge point
An arithmetic sequence has a constant difference \(d\) between consecutive terms:

$$ a_{n} - a_{n-1} = d $$

Analyze the first sequence

Using the Arithmetic Sequences knowledge point
For the sequence \(2, 6, 18, 54\):

$$
LATEXBLOCK0
$$

The differences are not constant.

Analyze the second sequence

Using the Arithmetic Sequences knowledge point
For the sequence \(5, 9, 13, 17\):

$$
LATEXBLOCK1
$$

The common difference is \(d = 4\).

Analyze the third sequence

Using the Arithmetic Sequences knowledge point
For the sequence \(3, 9, 27, 81\):

$$
LATEXBLOCK2
$$

The differences are not constant.

Analyze the fourth sequence

Using the Arithmetic Sequences knowledge point
For the sequence \(4, 8, 16, 32\):

$$
LATEXBLOCK3
$$

The differences are not constant.

Answer:

• (A) 2, 6, 18, 54
• (B) 5, 9, 13, 17 (Correct answer)
• (C) 3, 9, 27, 81
• (D) 4, 8, 16, 32