Enter the next two terms of the sequence.
-5,-2,-7,-9,-16,

The given sequence is:

\[
-5, -2, -7, -9, -16, \ldots
\]

Let's analyze the differences between consecutive terms:

\[
-2 - (-5) = 3
\]
\[
-7 - (-2) = -5
\]
\[
-9 - (-7) = -2
\]
\[
-16 - (-9) = -7
\]

So the differences between terms are: \(3, -5, -2, -7\).

Now, let's see if the differences follow a pattern. The second differences (differences of the differences) are:

\[
-5 - 3 = -8
\]
\[
-2 - (-5) = 3
\]
\[
-7 - (-2) = -5
\]

These second differences don't show a constant value, so the sequence might involve alternating steps or a more complex pattern. However, from observation, it appears that the first set of differences may repeat. Following the established differences, we can predict the next terms:

- The next difference should be \(-2 + (-8) = -10\), so the next term is:
  \[
  -16 + (-10) = -26
  \]

- The next difference after that would be \(-26 + (-3) = -29\).

Thus, the next two terms of the sequence are:  
**-26, -29**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How can we determine if a sequence is arithmetic or geometric?
2. What are second differences, and when are they useful?
3. How can you find the formula for a sequence?
4. What is the difference between a finite and infinite sequence?
5. How can alternating patterns in sequences be identified?

**Tip**: Checking the differences between consecutive terms is a useful way to find patterns in sequences.

Enter the next two terms of the sequence: -5, -2, -7, -9, -16,

Discover how to find the next two terms of the sequence -5, -2, -7, -9, -16 by analyzing the differences between consecutive terms. This step-by-step explanation covers patterns in sequences, including alternating differences, and is suitable for Grades 7-10.

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