Questions and Answers
What is the formula for the nth term of the geometric sequence shown on the graph?
C
What is the common ratio of the geometric sequence -96, 48, -24, 12, -6,...?
B
Which formula can be used to find the nth term of the geometric sequence 1/6, 1, 6?
D
Which of the following shows the correct relationship between the terms f, g, h in a geometric sequence?
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Which of the following classifies the sequence written by Fiona?
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What is the next term in the sequence that ends with -324?
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Which formula can be used to find the nth term of a geometric sequence where the fifth term is given and the common ratio is provided?
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What is the common ratio of the sequence 2/3, 1/6?
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Which student wrote a geometric sequence?
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What is the common ratio of the geometric sequence -2, 4, -8, 16, -32,...?
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Which student wrote a geometric sequence?
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What is the seventh term defined by the given terms?
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When is a sequence considered geometric?
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Which formula can be used to find the nth term in a geometric sequence where some terms are given?
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Study Notes
Geometric Sequences Overview
- A geometric sequence consists of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio.
- The nth term can be represented using the formula: ( a_n = a_1 \cdot r^{(n-1)} ), where ( a_1 ) is the first term, ( r ) is the common ratio, and ( n ) is the term number.
Common Ratio
- The common ratio is calculated by dividing any term in the sequence by the preceding term.
- Examples include:
- Sequence: -96, 48, -24, 12, -6... has a common ratio of -0.5.
- Sequence: -2, 4, -8, 16, -32... has a common ratio of -2.
- For the sequence 2/3, 1/6, the common ratio is 1/4.
Finding nth Term
- The formula for finding the nth term requires knowledge of the first term and the common ratio.
- In some cases, specific values for certain terms (like the fifth term) are provided to help derive the formula.
Relationships in Sequences
- The relationship between the first three terms of a geometric sequence can be expressed in terms of their divisibility by the common ratio.
Classifying Sequences
- Sequences can be classified based on their ratios; a sequence that maintains a consistent ratio qualifies as a geometric sequence.
- Different students can record different sequences, and only some of them may be geometric based on the behavior of their terms.
Identifying Geometric Sequences
- To determine if a sequence is geometric, check for a constant ratio between consecutive terms.
- Not all sequences written by students will be classified as geometric, emphasizing the need for verification.
Additional Notes
- Sequences can have negative terms, and geometric sequences can have alternating signs depending on the common ratio.
- When given a defined formula, one can compute any term in the sequence, including the seventh term based on the defined parameters.
Studying That Suits You
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Description
Test your knowledge of geometric sequences with this set of flashcards. Each card presents a question about the characteristics and formulas related to geometric sequences. Perfect for students looking to reinforce their understanding of this essential mathematical concept.
