Question

tell whether the sequence is arithmetic. if it is, identify the common difference.
6, 8, 10, 12, ...
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the sequence is arithmetic and has a common difference of

b. the sequence is not arithmetic.

Explanation:

Step1: Recall Arithmetic Sequence Definition

An arithmetic sequence has a constant difference between consecutive terms. The formula for the difference between consecutive terms is \( a_{n + 1}-a_{n}\), where \( a_{n+1}\) is the next term and \( a_{n}\) is the current term.

Step2: Calculate Differences Between Terms

• For the first two terms: \( 8 - 6 = 2\)
• For the next two terms: \( 10 - 8 = 2\)
• For the following two terms: \( 12 - 10 = 2\)

Since the difference between consecutive terms is constant (2), the sequence is arithmetic with a common difference of 2.

Answer:

A. The sequence is arithmetic and has a common difference of \( 2 \).