We are dealing with a sequence: 

\[
-8 + (-12) + (-16) + \dots + (-308)
\]

This sequence is an **arithmetic sequence** (also called an arithmetic progression) because the difference between consecutive terms is constant.

### Step 1: Identify the first term and common difference
- The first term \(a = -8\)
- The common difference \(d = -12 - (-8) = -4\)

### Step 2: Identify the last term
- The last term is \(l = -308\)

### Step 3: Find the number of terms \(n\)
We can use the formula for the \(n\)-th term of an arithmetic sequence:

\[
l = a + (n - 1) \cdot d
\]

Substitute the values for \(l\), \(a\), and \(d\):

\[
-308 = -8 + (n - 1) \cdot (-4)
\]

Simplifying:

\[
-308 + 8 = (n - 1) \cdot (-4)
\]
\[
-300 = (n - 1) \cdot (-4)
\]
\[
n - 1 = \frac{-300}{-4} = 75
\]
\[
n = 76
\]

There are 76 terms in the sequence.

### Step 4: Find the sum of the sequence
The sum \(S_n\) of an arithmetic sequence is given by:

\[
S_n = \frac{n}{2} \cdot (a + l)
\]

Substitute the values for \(n\), \(a\), and \(l\):

\[
S_{76} = \frac{76}{2} \cdot (-8 + (-308))
\]
\[
S_{76} = 38 \cdot (-316)
\]
\[
S_{76} = -12008
\]

### Final Answer:
The sum of the sequence is \(-12008\).

---

Would you like more details on any step or have any questions?

Here are 5 related questions to explore further:
1. How do you find the sum of a geometric sequence?
2. What are some real-life examples of arithmetic sequences?
3. How does the sum formula for arithmetic sequences change with different common differences?
4. What if the terms alternated signs, how would that affect the sum?
5. Can you derive the formula for the \(n\)-th term of an arithmetic sequence?

**Tip:** When solving arithmetic sequence problems, always double-check the common difference and the number of terms for accuracy.

Learn how to find the sum of the arithmetic sequence -8 + (-12) + (-16) ... + (-308) with a detailed step-by-step solution. This problem covers key concepts such as identifying the first term, common difference, number of terms, and applying the sum formula for an arithmetic sequence. Suitable for students in Grades 9-10.

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