Questions: Check whether the sequence is arithmetic. If so, find the common difference (d). 6, 9, 12, 15, 18 ... Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The common difference is (square) (Simplify your answer.) B. The sequence is not arithmetic.

Check whether the sequence is arithmetic. If so, find the common difference (d).

6, 9, 12, 15, 18 ...

Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The common difference is (square) (Simplify your answer.)
B. The sequence is not arithmetic.

Transcript text: Check whether the sequence is arithmetic. If so, find the common difference $d$. \[ 6,9,12,15,18 \ldots \] Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The common difference is $\square$ (Simplify your answer.) B. The sequence is not arithmetic.

Solution

Solution Steps

To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant. If it is, the sequence is arithmetic, and the common difference $d$ is that constant difference.

Step 1: Identify the Sequence

The given sequence is $6, 9, 12, 15, 18$.

Step 2: Calculate the Differences

We calculate the differences between consecutive terms: \[ 9 - 6 = 3, \quad 12 - 9 = 3, \quad 15 - 12 = 3, \quad 18 - 15 = 3 \] Thus, the differences are $3, 3, 3, 3$.

Step 3: Check for Arithmetic Sequence

Since the differences between all consecutive terms are equal, we conclude that the sequence is arithmetic.

Step 4: Determine the Common Difference

The common difference $d$ is $3$.