Question

which of these sequences are arithmetic? check all that apply.

-5, -3, 3, 13, 27, ...
0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, ...
7, 14, 28, 56, 112, ...
27, 40, 53, 66, 79, ...
1, 2, 4, 8, ...

Explanation:

Define arithmetic sequences

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

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

Analyze the first sequence

Using the Arithmetic Sequences knowledge point
For \(-5, -3, 3, 13, 27, \dots\):

$$
LATEXBLOCK0
$$

Since \(2
eq 6\), this sequence is not arithmetic.

Analyze the second sequence

Using the Arithmetic Sequences knowledge point
For \(0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \dots\):

$$
LATEXBLOCK1
$$

Since the common difference is constantly \(\frac{1}{4}\), this sequence is arithmetic.

Analyze the third and fifth sequences

Using the Arithmetic Sequences knowledge point
For \(7, 14, 28, 56, 112, \dots\):

$$
LATEXBLOCK2
$$

For \(1, 2, 4, 8, \dots\):

$$
LATEXBLOCK3
$$

Neither sequence is arithmetic (both are geometric with common ratios \(2\)).

Analyze the fourth sequence

Using the Arithmetic Sequences knowledge point
For \(27, 40, 53, 66, 79, \dots\):

$$
LATEXBLOCK4
$$

Since the common difference is constantly \(13\), this sequence is arithmetic.

Answer:

• \(-5, -3, 3, 13, 27, \dots\)
• \(0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \dots\) (Correct answer)
• \(7, 14, 28, 56, 112, \dots\)
• \(27, 40, 53, 66, 79, \dots\) (Correct answer)
• \(1, 2, 4, 8, \dots\)