Math Problem Statement
Solution
The image contains a problem related to geometric sequences (deret geometri). The question appears to be:
"Tiga suku pertama deret geometri adalah , , dan . Pernyataan yang benar adalah ...."
This translates to: "The first three terms of a geometric sequence are , , and . 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 between the second and first term is equal to the ratio between the third and second term:
Substitute the terms:
Step 2: Solve the equation
Now, we solve the equation:
To solve this, cross multiply:
Expanding both sides:
Step 3: Simplify the equation
Cancel out the terms:
Move all terms involving to one side:
Divide both sides by :
Step 4: Verify the solution
Substitute into the original terms:
- First term:
- Second term:
- Third term:
The first three terms of the geometric sequence are 2, -6, and 18. Now, verify the common ratio :
Since the common ratio is constant, the sequence is valid.
Step 5: Conclusion
The correct value of is 2, and the ratio is . Therefore, the statement that is correct is:
- The second term is (not 6 as indicated in the options).
- The third term is .
- The ratio is .
Would you like more details or have any other questions? Here are some follow-up questions you might find interesting:
- What are the properties of a geometric sequence?
- How can you find the sum of the first terms of a geometric sequence?
- What is the significance of a common ratio in geometric sequences?
- Can a geometric sequence have a common ratio of zero?
- 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.
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Math Problem Analysis
Mathematical Concepts
Geometric Sequences
Ratios
Formulas
r = Second Term / First Term = Third Term / Second Term
Theorems
Geometric Sequence Ratio Formula
Suitable Grade Level
Grades 9-12
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