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The image contains a problem related to geometric sequences (deret geometri). The question appears to be:

"Tiga suku pertama deret geometri adalah \(a\), \(2a - 10\), dan \(4a + 10\). Pernyataan yang benar adalah ...."

This translates to:
"The first three terms of a geometric sequence are \(a\), \(2a - 10\), and \(4a + 10\). Which of the following statements is true?"

Let's solve this problem step by step:

### Step 1: Identify the formula for a geometric sequence
In a geometric sequence, the ratio between consecutive terms is constant. That is, the ratio \(r\) between the second and first term is equal to the ratio between the third and second term:

\[
r = \frac{\text{Second term}}{\text{First term}} = \frac{\text{Third term}}{\text{Second term}}
\]

Substitute the terms:
\[
r = \frac{2a - 10}{a} = \frac{4a + 10}{2a - 10}
\]

### Step 2: Solve the equation
Now, we solve the equation:

\[
\frac{2a - 10}{a} = \frac{4a + 10}{2a - 10}
\]

To solve this, cross multiply:

\[
(2a - 10)(2a - 10) = a(4a + 10)
\]

Expanding both sides:

\[
(2a - 10)^2 = a(4a + 10)
\]

\[
4a^2 - 40a + 100 = 4a^2 + 10a
\]

### Step 3: Simplify the equation
Cancel out the \(4a^2\) terms:

\[
-40a + 100 = 10a
\]

Move all terms involving \(a\) to one side:

\[
-40a - 10a = -100
\]

\[
-50a = -100
\]

Divide both sides by \(-50\):

\[
a = 2
\]

### Step 4: Verify the solution
Substitute \(a = 2\) into the original terms:

- First term: \(a = 2\)
- Second term: \(2a - 10 = 2(2) - 10 = 4 - 10 = -6\)
- Third term: \(4a + 10 = 4(2) + 10 = 8 + 10 = 18\)

The first three terms of the geometric sequence are 2, -6, and 18. Now, verify the common ratio \(r\):

\[
r = \frac{-6}{2} = -3, \quad r = \frac{18}{-6} = -3
\]

Since the common ratio is constant, the sequence is valid.

### Step 5: Conclusion
The correct value of \(a\) is 2, and the ratio \(r\) is \(-3\). Therefore, the statement that is correct is:
- The second term is \(-6\) (not 6 as indicated in the options).
- The third term is \(18\).
- The ratio is \(-3\).

Would you like more details or have any other questions? Here are some follow-up questions you might find interesting:

1. What are the properties of a geometric sequence?
2. How can you find the sum of the first \(n\) terms of a geometric sequence?
3. What is the significance of a common ratio in geometric sequences?
4. Can a geometric sequence have a common ratio of zero?
5. How does a geometric sequence differ from an arithmetic sequence?

**Tip:** In geometric sequences, always ensure the ratio between consecutive terms is constant before assuming a sequence is geometric.

Tiga suku pertama deret geometri adalah a, 2a - 10, dan 4a + 10. Pernyataan yang benar adalah ....

Solve the geometric sequence problem where the first three terms are a, 2a - 10, and 4a + 10. Learn how to find the common ratio and solve for 'a'. This problem covers key algebraic concepts, including the geometric sequence ratio formula. Suitable for students in Grades 9-12.

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