Question

Find the next four terms of each arithmetic sequence.

-6, -2, 2, …

Short answer

The next four terms of the arithmetic sequence are6, 10, 14, 18.

Step-by-step solution

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 $\left(-2\right)-\left(-6\right)=-2+6=4$

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

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.