Question

which of the following is an arithmetic sequence?

• (3, 5, 7, 9, \dots)
• (3, 5, 8, 11, \dots)
• (64, 32, 16, 8, \dots)
• (-6, -9, -10, \dots)

Explanation:

Step1: Define arithmetic sequence

An arithmetic sequence has a constant difference between consecutive terms.

Step2: Test the first option

Calculate differences for \(3, 5, 7, 9, \dots\):

$$5 - 3 = 2$$

$$7 - 5 = 2$$

$$9 - 7 = 2$$

The difference is constant.

Step3: Test the second option

Calculate differences for \(3, 5, 8, 11, \dots\):

$$5 - 3 = 2$$

$$8 - 5 = 3$$

The difference is not constant.

Step4: Test the third option

Calculate differences for \(64, 32, 16, 8, \dots\):

$$32 - 64 = -32$$

$$16 - 32 = -16$$

The difference is not constant.

Step5: Test the fourth option

Calculate differences for \(-6, -9, -10, \dots\):

$$-9 - (-6) = -3$$

$$-10 - (-9) = -1$$

The difference is not constant.

Answer:

A. \(3, 5, 7, 9, \dots\)