https://file.aiquickdraw.com/mathbot/file/1727059984641m2salfgf.jpg

The question asks for the sum of the first ten terms of an arithmetic sequence (deret aritmatika) where the first term is 20 and the sixth term is 40.

To solve this, we can follow these steps:

1. **Identify the common difference (d):**

   The nth term of an arithmetic sequence is given by the formula:
   \[
   a_n = a_1 + (n - 1) \cdot d
   \]
   We know that \( a_1 = 20 \) (the first term) and \( a_6 = 40 \) (the sixth term). Substituting into the formula for \( a_6 \):
   \[
   a_6 = a_1 + (6 - 1) \cdot d
   \]
   \[
   40 = 20 + 5 \cdot d
   \]
   \[
   40 - 20 = 5d
   \]
   \[
   d = \frac{20}{5} = 4
   \]
   So, the common difference \( d = 4 \).

2. **Find the sum of the first 10 terms:**

   The sum \( S_n \) of the first \( n \) terms of an arithmetic sequence is given by:
   \[
   S_n = \frac{n}{2} \cdot (a_1 + a_n)
   \]
   We want to find \( S_{10} \) (the sum of the first 10 terms). First, calculate the 10th term \( a_{10} \):
   \[
   a_{10} = a_1 + (10 - 1) \cdot d = 20 + 9 \cdot 4 = 20 + 36 = 56
   \]
   Now, calculate the sum:
   \[
   S_{10} = \frac{10}{2} \cdot (20 + 56) = 5 \cdot 76 = 380
   \]

Thus, the sum of the first ten terms is **380**.

Would you like further details or have any questions?

Here are 5 related questions to expand this concept:
1. How would the sum change if the common difference were 5 instead of 4?
2. What is the formula for finding the nth term of a geometric sequence?
3. How can we derive the formula for the sum of an arithmetic sequence?
4. If the first term were negative, how would that affect the sum of the first 10 terms?
5. Can we calculate the sum of the first 20 terms given the same arithmetic sequence?

**Tip:** In arithmetic sequences, knowing the first term and the common difference lets you find any term in the sequence using a simple formula!

Dari suatu deret aritmatika, diketahui suku pertama adalah 20 dan suku keenam adalah 40. Jumlah sepuluh suku pertama dari deret tersebut adalah ...

Learn how to find the sum of the first 10 terms of an arithmetic sequence where the first term is 20 and the sixth term is 40. Detailed step-by-step solution provided with formulas for finding the common difference and calculating the sum of terms.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation