Geometric Sequences Quiz Flashcards

What is the formula for the nth term of the geometric sequence shown on the graph?

What is the common ratio of the geometric sequence -96, 48, -24, 12, -6,...?

Which formula can be used to find the nth term of the geometric sequence 1/6, 1, 6?

Which of the following shows the correct relationship between the terms f, g, h in a geometric sequence?

Which of the following classifies the sequence written by Fiona?

What is the next term in the sequence that ends with -324?

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?

What is the common ratio of the sequence 2/3, 1/6?

Which student wrote a geometric sequence?

What is the common ratio of the geometric sequence -2, 4, -8, 16, -32,...?

Which student wrote a geometric sequence?

What is the seventh term defined by the given terms?

When is a sequence considered geometric?

Which formula can be used to find the nth term in a geometric sequence where some terms are given?

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.

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.