This is an arithmetic sequence where the terms decrease by a constant value. Let’s find the sum step by step.

Step 1: Identify the sequence

The sequence starts at $a = 8$ and decreases by a common difference $d = -6$. The general term of the sequence is given by: $a_n = a + (n-1)d$ We are summing until the last term $a_n = -58$.

Step 2: Find the number of terms ($n$)

Set the general term equal to the last term ($-58$) and solve for $n$: $-58 = 8 + (n-1)(-6)$ Simplify: $-58 = 8 - 6(n-1)$ $-58 = 8 - 6n + 6$ $-58 = 14 - 6n$ $-72 = -6n$ $n = 12$

Step 3: Use the sum formula

The sum of an arithmetic sequence is given by: $S_n = \frac{n}{2} (a + a_n)$ Substitute $n = 12$, $a = 8$, and $a_n = -58$: $S_{12} = \frac{12}{2} (8 + (-58))$ $S_{12} = 6 \cdot (-50)$ $S_{12} = -300$

Final Answer:

The sum of the sequence is: $\boxed{-300}$

Would you like further details or explanations?

Questions to Expand:

1. What is an arithmetic sequence, and how is it defined?
2. How is the formula for the $n$-th term of an arithmetic sequence derived?
3. Can the sum formula $S_n$ be applied to geometric sequences?
4. How do we find the common difference ($d$) in a sequence?
5. What are real-life applications of arithmetic sequences?

Tip:

Always verify the number of terms ($n$) before applying the sum formula to avoid errors!