Identify the missing terms in the sequence below.$-18, [?], [?], -45, -54$

We are given the sequence: $ -18, \, [?], \, [?], \, -45, \, -54 $.

To identify the missing terms, let's check if there's a constant difference between consecutive terms. The differences between consecutive terms would help us understand the pattern.

### Step 1: Find the difference between the last two known terms
The difference between $-54$ and $-45$ is:
\[
-54 - (-45) = -54 + 45 = -9
\]
Thus, the difference between $-54$ and $-45$ is $-9$.

### Step 2: Check if the difference is consistent
If the difference is consistent, then we can apply the same difference to find the previous terms. Since $-45 - (-9) = -54$, we expect a common difference of $-9$ throughout the sequence.

### Step 3: Calculate the missing terms
1. To find the term before $-45$, subtract $-9$ from $-45$:
\[
-45 - 9 = -36
\]
Thus, the missing term before $-45$ is $-36$.

2. To find the term before $-36$, subtract $-9$ from $-36$:
\[
-36 - 9 = -27
\]
Thus, the missing term before $-36$ is $-27$.

3. To find the term before $-27$, subtract $-9$ from $-27$:
\[
-27 - 9 = -18
\]
This confirms the first term of the sequence is $-18$, as given.

### Final Sequence:
The complete sequence is:
\[
-18, \, -27, \, -36, \, -45, \, -54
\]

### Conclusion:
The missing terms in the sequence are $ -27 $ and $ -36 $.

Would you like further details on how to identify patterns in sequences?

Here are some related questions:
1. How do you determine if a sequence is arithmetic?
2. What is the general formula for finding the $n$-th term of an arithmetic sequence?
3. How do you distinguish between arithmetic and geometric sequences?
4. How would you find the sum of an arithmetic sequence?
5. Can you explain how to handle sequences where the difference between terms is not constant?

**Tip**: In an arithmetic sequence, the difference between any two consecutive terms is constant. Use this property to find missing terms easily.

Learn how to identify missing terms in an arithmetic sequence -18, [?], [?], -45, -54 with a detailed step-by-step solution. This problem covers key concepts in arithmetic sequences, including finding the common difference and determining missing terms. Suitable for students in Grades 7-9.

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