Q. 17 - Algebra 2

Question

Find the next four terms of each arithmetic sequence.

 -6, -2, 2, …

Step-by-Step Solution

Answer

The next four terms of the arithmetic sequence are 6, 10, 14, 18.

Step 1. Given Information.

The given arithmetic sequence is -6, -2, 2, …

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  $(-2)-(-6)=-2+6=4$

The difference between the next two terms is  $2-(-2)=2+2=4$

So, the common difference is 4.

 

The next term in the arithmetic sequence is  $2+4=6$

The next term in the arithmetic sequence is  $6+4=10$

The next term in the arithmetic sequence is  $10+4=14$

The next term in the arithmetic sequence is  $14+4=18$

Step 3. Conclusion .

Hence, the next four terms of the arithmetic sequence are 6, 10, 14, 18.