Math Problem Statement
tentukan suku ke-10 dari barisan bilangan 90,45, 45
Solution
The problem asks to find the 10th term in the sequence that starts with:
Identifying the Sequence:
From the given terms, the pattern suggests that each term is halved successively after the second term:
This indicates that the common ratio between consecutive terms is , forming a geometric sequence after the first two terms.
General Formula for the Sequence:
The first term () is , and the second term () is . The terms after the second follow the form of:
Finding the 10th Term:
Now, we want to find the 10th term. For :
Thus, the 10th term of the sequence is .
Let me know if you need any further explanation or more details.
Related Questions:
- What is the 5th term in this sequence?
- How do you determine if a sequence is geometric?
- What is the sum of the first 10 terms in this geometric sequence?
- How does the common ratio affect the behavior of a geometric sequence?
- Can this sequence have a limit as approaches infinity?
Tip:
In geometric sequences, if the common ratio is less than 1, the terms approach 0 as increases.
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Math Problem Analysis
Mathematical Concepts
Geometric Sequence
Ratio
Formulas
General term of geometric sequence: a_n = a_1 * r^(n-1)
For this sequence: a_n = 45 * (1/2)^(n-2) for n >= 2
Theorems
Geometric progression with a common ratio less than 1 tends to zero
Suitable Grade Level
Grades 9-11
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