Question

Find the next four terms of each arithmetic sequence.

3, 1, -1, …

Short answer

The next four terms of the arithmetic sequence are-3, -5, -7, -9.

Step-by-step solution

Step 1. Given Information.

The given arithmetic sequence is 3, 1, -1, …

Step 2. Calculation.

A sequence is said to be arithmetic when the difference between the consecutive terms is always the same.

Here the difference between the first two terms is $1-3=-2$

The difference between the next two terms is $-1-1=-2$

So, the common difference is -2.

The next term in the arithmetic sequence is $-1-2=-3$

The next term in the arithmetic sequence is $-3-2=-5$

The next term in the arithmetic sequence is $-5-2=-7$

The next term in the arithmetic sequence is $-7-2=-9$

Step 3. Conclusion.

Hence, the next four terms of the arithmetic sequence are -3, -5, -7, -9.