Q16. - Algebra 2

Question

Find the next four terms of each arithmetic sequence.

 

31, 24, 17, …

Step-by-Step Solution

Answer

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

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.