Problem

Check whether the sequence is arithmetic. If so, find the common difference $d$.
\[
2,6,9,13,16 \ldots
\]
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The common difference is (Simplify your answer.)
B. The sequence is not arithmetic.

Answer

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Answer

Final Answer: \(\boxed{\text{The sequence is not arithmetic.}}\)

Steps

Step 1 :An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is called the common difference. To check if a sequence is arithmetic, we subtract the second term from the first term, the third term from the second term, and so on, and check if the differences are the same.

Step 2 :In this case, we have the sequence 2, 6, 9, 13, 16. Let's calculate the differences between consecutive terms.

Step 3 :The differences between consecutive terms are 4, 3, 4, 3.

Step 4 :The differences between consecutive terms are not the same. Therefore, the sequence is not arithmetic.

Step 5 :Final Answer: \(\boxed{\text{The sequence is not arithmetic.}}\)

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