Question

the first three terms of an arithmetic sequence are as follows.
-8, -1, 6
find the next two terms of this sequence.
-8, -1, 6, \boxed{}, \boxed{}

Explanation:

Step1: Find the common difference

To find the common difference \(d\) in an arithmetic sequence, we subtract consecutive terms. Let's take the second term minus the first term: \(-1 - (-8) = -1 + 8 = 7\). Let's check with the third term minus the second term: \(6 - (-1) = 6 + 1 = 7\). So the common difference \(d = 7\).

Step2: Find the fourth term

To find the fourth term, we add the common difference to the third term. The third term is \(6\), so the fourth term is \(6 + 7 = 13\).

Step3: Find the fifth term

To find the fifth term, we add the common difference to the fourth term. The fourth term is \(13\), so the fifth term is \(13 + 7 = 20\).

Answer:

The next two terms are \(13\) and \(20\).