Questions: Determine if the given sequence is an arithmetic sequence. If it is, find the common difference, (6,-9,12,-15, ldots) Is this an arithmetic sequence? Yes No

Solution Steps

To determine if a sequence is arithmetic, we need to check if the difference between consecutive terms is constant. Calculate the differences between each pair of consecutive terms and see if they are all the same. If they are, the sequence is arithmetic, and the common difference is that constant value.

The given sequence is \(6, -9, 12, -15, \ldots\).

Calculate the differences between each pair of consecutive terms:

• Difference between \(-9\) and \(6\) is \(-9 - 6 = -15\).
• Difference between \(12\) and \(-9\) is \(12 - (-9) = 21\).
• Difference between \(-15\) and \(12\) is \(-15 - 12 = -27\).

The differences are \(-15\), \(21\), and \(-27\). Since these differences are not equal, the sequence does not have a constant difference.

Final Answer