Lesson 6.2 Geometric Sequences
Flashcard
•
Mathematics
•
8th - 9th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a geometric sequence?
Back
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.
2.
FLASHCARD QUESTION
Front
How do you find the first four terms of a geometric sequence given the first term and the common ratio?
Back
To find the first four terms, start with the first term and multiply by the common ratio for each subsequent term. For example, if a1 = 10 and the common ratio is 3, the terms are: 10, 30, 90, 270.
3.
FLASHCARD QUESTION
Front
What is the explicit formula for a geometric sequence?
Back
4.
FLASHCARD QUESTION
Front
What is the recursive rule for a geometric sequence?
Back
The recursive rule for a geometric sequence is defined as: a1 = first term; an = an-1 * r, where r is the common ratio.
5.
FLASHCARD QUESTION
Front
How do you identify the common ratio in a geometric sequence?
Back
The common ratio can be found by dividing any term by the previous term. For example, in the sequence 64, 16, 4, the common ratio is 1/4 (16/64 or 4/16).
6.
FLASHCARD QUESTION
Front
What is the difference between a geometric sequence and an arithmetic sequence?
Back
In a geometric sequence, each term is multiplied by a constant (common ratio), while in an arithmetic sequence, each term is added to a constant (common difference).
7.
FLASHCARD QUESTION
Front
How do you find the next term in a geometric sequence?
Back
To find the next term, multiply the last known term by the common ratio. For example, if the last term is 90 and the common ratio is 3, the next term is 90 * 3 = 270.
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