Problem

Tell whether the sequence is arithmetic. If it is, identify the common difference.
\[
2,11,20,29, \ldots
\]
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.

Answer

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Answer

Final Answer: The sequence is arithmetic and has a common difference of \(\boxed{9}\).

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 determine if the given sequence is arithmetic, we need to check if the difference between consecutive terms is the same throughout the sequence.

Step 2 :The given sequence is \(2,11,20,29, \ldots\)

Step 3 :Calculate the differences between consecutive terms: \(11-2=9\), \(20-11=9\), \(29-20=9\)

Step 4 :The differences between each consecutive pair of terms in the sequence is consistently 9.

Step 5 :Final Answer: The sequence is arithmetic and has a common difference of \(\boxed{9}\).

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