Math Problem Statement
Let {ai} with index starting at 0 represent a geometric sequence. If a7 = 7 and a8 = 28, what is a9?
Solution
Given that represents a geometric sequence, we know that the ratio between consecutive terms is constant. Let the common ratio be denoted as .
The terms provided are:
In a geometric sequence, we have the relation: Using this, we can express in terms of : Substituting the given values: Solving for :
Now, to find , we use the fact that: Substitute and :
Thus, .
Would you like further details or have any questions?
Here are 5 related questions:
- How is the common ratio in a geometric sequence defined?
- What is the general formula for the -th term of a geometric sequence?
- How can you determine if a sequence is geometric from its terms?
- What happens to a geometric sequence if the common ratio is less than 1?
- How do geometric sequences differ from arithmetic sequences?
Tip: In geometric sequences, each term is found by multiplying the previous term by a constant factor (the common ratio).
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometric Sequences
Ratios
Formulas
a_{n+1} = a_n * r
r = a_{n+1} / a_n
Theorems
Geometric Sequence Definition
Suitable Grade Level
Grades 8-10
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