Question

In the following exercises, determine if each sequence is arithmetic, and if so, indicate the common difference.

$13,9,5,1,-3,-7,.....$

Short answer

The sequence $13,9,5,1,-3,-7,.....$is arithmetic with common difference $-4$.

Step-by-step solution

Step 1. Given information

The sequence is $13,9,5,1,-3,-7,.....$.

We have to determine if this sequence is arithmetic, and if so, we have to indicate the common difference.

Step 2. Find the difference between the consecutive terms

Find the difference between each term and its preceding term.

$$\begin{gathered} 9-13=-4 \\ 5-9=-4 \\ 1-5=-4 \\ -3-1=-4 \\ -7-(-3)=-4 \end{gathered}$$

Step 3. Check if the difference is constant

Since the difference is found to be constant, this sequence is arithmetic.

This constant difference is called the common difference.

Therefore, the common difference is $-4$.