What is a geometric sequence?
Geometric Sequences

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•
Mathematics
•
9th 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 first four terms of a geometric sequence given the formula a_n = a * r^(n-1)?
Back
Substitute n = 1, 2, 3, and 4 into the formula to find the first four terms.
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
Given the sequence 3, 15, 75, how do you find the common ratio?
Back
Divide any term by the previous term: 15/3 = 5 or 75/15 = 5. The common ratio is 5.
5.
FLASHCARD QUESTION
Front
What is the explicit formula for a geometric sequence?
Back
The explicit formula is a_n = a * r^(n-1), where a is the first term and r is the common ratio.
6.
FLASHCARD QUESTION
Front
How can you determine if a sequence is geometric?
Back
Check if the ratio of consecutive terms is constant.
7.
FLASHCARD QUESTION
Front
What is the first term of the geometric sequence defined by a_n = 4(5)^(n-1)?
Back
The first term (when n=1) is 4.
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