Question

Find the next four terms of each arithmetic sequence.

31, 24, 17, …

Short answer

The next four terms of the arithmetic sequence are10, 3, -4, -11.

Step-by-step solution

Step 1. Given Information.

The given arithmetic sequence is 31, 24, 17, …

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 $24-31=-7$

The difference between the next two terms is $17-24=-7$

So, the common difference is -7.

The next term in the arithmetic sequence is $17-7=10$

The next term in the arithmetic sequence is $10-7=3$

The next term in the arithmetic sequence is $3-7=-4$

The next term in the arithmetic sequence is $-4-7=-11$

Step 3. Conclusion.

Hence, the next four terms of the arithmetic sequence are 10, 3, -4, -11.