Problem 88
Question
What is a geometric sequence? Give an example with your explanation.
Step-by-Step Solution
Verified Answer
A geometric sequence is a sequence where each term is found by multiplying the preceding term by a fixed, non-zero number called the common ratio. For example, in the sequence 2, 4, 8, 16, 32,... the common ratio is 2.
1Step 1: Explain Geometric sequence
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
2Step 2: Common ratio(how to determine it)
The common ratio can be determined in a geometric sequence by dividing any term by the preceding term. The quotient remains constant throughout the sequence.
3Step 3: Provide an example
One example of a geometric sequence is 2, 4, 8, 16, 32,... In this sequence, each term is found by multiplying the preceding term by 2. So, the common ratio is 2.
Other exercises in this chapter
Problem 86
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View solution Problem 87
Exercises \(85-87\) will help you prepare for the material covered in the next section. Use the formula \(a_{n}-a_{1} 3^{n-1}\) to find the seventh term of the
View solution Problem 89
What is the common ratio in a geometric sequence?
View solution Problem 90
Explain how to find the general term of a geometric sequence.
View solution