What is a geometric sequence?
Geometric Sequences

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•
Mathematics
•
7th - 10th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
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 nth term of a geometric sequence?
Back
The nth term of a geometric sequence can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.
3.
FLASHCARD QUESTION
Front
What is the common ratio in a geometric sequence?
Back
The common ratio is the factor by which we multiply each term to get the next term in the sequence.
4.
FLASHCARD QUESTION
Front
If a_3 = 224 and r = -1/2, how do you find a_1?
Back
Use the formula a_n = a_1 * r^(n-1). For a_3, we have 224 = a_1 * (-1/2)^(3-1). Solve for a_1.
5.
FLASHCARD QUESTION
Front
Find the first four terms of the sequence given a_n = 4(5)^(n-1).
Back
The first four terms are: 4, 20, 100, 500.
6.
FLASHCARD QUESTION
Front
What is the formula for the nth term of a geometric sequence?
Back
The formula is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.
7.
FLASHCARD QUESTION
Front
Given a_1 = 10 and a_n = a_(n-1) * 3, what are the first four terms?
Back
The first four terms are: 10, 30, 90, 270.
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