Math Problem Statement
Solution
We are given that the 17th term of a geometric sequence is 15, and the common ratio is . The task is to find the 18th term.
In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio. So, the relationship between consecutive terms is:
To find the 18th term (), we use the formula:
Given that and :
Thus, the 18th term is , which matches the first answer option.
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Related Questions:
- What is the general formula for the -th term of a geometric sequence?
- How do you find the sum of a finite geometric series?
- What happens to the terms of a geometric sequence if the common ratio is negative?
- How does the common ratio affect the convergence of an infinite geometric sequence?
- Can a geometric sequence have a common ratio of 1 or 0?
Tip: In geometric sequences, if the common ratio is less than 1, the terms decrease as the sequence progresses.
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Math Problem Analysis
Mathematical Concepts
Geometric Sequence
Common Ratio
Formulas
a_{n+1} = a_n * r
a_{18} = a_{17} * r
Theorems
Geometric Sequence Term Formula
Suitable Grade Level
Grades 8-10
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