The question is written in Indonesian and translates to:

"Determine the 10th term and the sum of the first 10 terms of the sequence: -15, -11, -7, ..."

This sequence is an arithmetic sequence because the difference between consecutive terms is constant.

Step 1: Identify the Common Difference

The first term ($a$) is $-15$, and the common difference ($d$) is: $d = -11 - (-15) = -11 + 15 = 4$

Step 2: Find the 10th Term

The formula for the $n$-th term of an arithmetic sequence is: $a_n = a + (n - 1) \cdot d$ For the 10th term ($a_{10}$): $a_{10} = -15 + (10 - 1) \cdot 4 = -15 + 9 \cdot 4 = -15 + 36 = 21$ So, the 10th term is 21.

Step 3: Calculate the Sum of the First 10 Terms

The formula for the sum of the first $n$ terms in an arithmetic sequence is: $S_n = \frac{n}{2} \cdot (2a + (n - 1) \cdot d)$ For the sum of the first 10 terms ($S_{10}$): $S_{10} = \frac{10}{2} \cdot (2 \cdot -15 + (10 - 1) \cdot 4)$ $S_{10} = 5 \cdot (-30 + 36) = 5 \cdot 6 = 30$ So, the sum of the first 10 terms is 30.

Final Answer

• The 10th term of the sequence is 21.
• The sum of the first 10 terms is 30.

Would you like further details or have any questions?

Related Questions:

1. What is the general formula for the sum of an arithmetic sequence?
2. How can you determine if a sequence is arithmetic or geometric?
3. What happens to the sequence if the common difference is negative?
4. How do you calculate the sum of terms if only the last term and common difference are known?
5. How do arithmetic sequences apply to real-world situations?

Tip:

For arithmetic sequences, knowing the common difference is key to finding any term or the sum up to any point.