To solve this arithmetic sequence problem, let's analyze the given terms:

The sequence starts as:
$-9, -2, 5$

Step 1: Find the common difference

The common difference $d$ in an arithmetic sequence is the difference between any two consecutive terms: $d = a_2 - a_1$ $d = -2 - (-9) = -2 + 9 = 7$

Verify the difference with the next term: $d = a_3 - a_2 = 5 - (-2) = 5 + 2 = 7$ Thus, the common difference $d = 7$.

Step 2: Find the next terms

Using the formula for the $n$-th term in an arithmetic sequence: $a_n = a_1 + (n-1)d$ We calculate the next two terms:

1. Fourth term ($a_4$): $a_4 = 5 + 7 = 12$
2. Fifth term ($a_5$): $a_5 = 12 + 7 = 19$

Final Answer:

The next two terms are: $12, 19$

Would you like further details or explanations?

Here are 5 related questions for further exploration:

1. How do you determine whether a sequence is arithmetic or not?
2. What is the general formula for the $n$-th term of an arithmetic sequence?
3. How can we calculate the sum of the first $n$ terms of an arithmetic sequence?
4. How would this problem differ if the sequence were geometric?
5. How can arithmetic sequences be applied to real-life problems?

Tip: Always verify the common difference by checking multiple consecutive terms to avoid mistakes.