The problem in the image asks for the sum of the first 30 terms of an arithmetic sequence:

$20 + 15 + 10 + 5 + \dots$

This is an arithmetic sequence where:

• The first term $a = 20$,
• The common difference $d = 15 - 20 = -5$,
• The number of terms $n = 30$.

The formula for the sum of the first $n$ terms of an arithmetic sequence is:

$S_n = \frac{n}{2} \times (2a + (n-1) \times d)$

Let's calculate the sum $S_{30}$.The sum of the first 30 terms of the arithmetic sequence is:

$S_{30} = -1575$

Thus, the correct answer is:

d. -1,575

Would you like more details or have any further questions?

Here are 5 related questions you could explore:

1. How is the formula for the sum of an arithmetic sequence derived?
2. What happens if the common difference $d$ is positive instead of negative?
3. How do you find the $n$-th term of an arithmetic sequence?
4. What are the applications of arithmetic sequences in real life?
5. How would the sum change if the number of terms increased to 50?

Tip: Always remember that in arithmetic sequences, the common difference remains constant between consecutive terms.