Write the next three terms of the arithmetic sequence. First term:   $17$17​  Common difference:  $-9$−9​The next three terms are  , , and .

1. ### Break Down the Problem

To find the next three terms of the arithmetic sequence, we need to start with the first term and use the common difference to generate subsequent terms.

2. ### Relevant Concepts

In an arithmetic sequence, each term can be found by adding the common difference to the previous term. The formula can be expressed as: $a_n = a_1 + (n - 1) \cdot d$ where:

• $a_n$ is the nth term,
• $a_1$ is the first term,
• $d$ is the common difference.

3. ### Analysis and Detail

1. Given:

   • First term, $a_1 = 17$
   • Common difference, $d = -9$

2. Calculate the next three terms:

   • Second term ($a_2$): $a_2 = a_1 + d = 17 + (-9) = 17 - 9 = 8$
   • Third term ($a_3$): $a_3 = a_2 + d = 8 + (-9) = 8 - 9 = -1$
   • Fourth term ($a_4$): $a_4 = a_3 + d = -1 + (-9) = -1 - 9 = -10$

4. ### Verify and Summarize

The calculations lead to:

• Second term: $8$
• Third term: $-1$
• Fourth term: $-10$

Final Answer

The next three terms of the arithmetic sequence are $8$, $-1$, and $-10$.