What is a geometric sequence?
Hon IM1 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 common ratio in a geometric sequence?
Back
The common ratio (r) can be found by dividing any term by the previous term: r = a_n / a_(n-1).
3.
FLASHCARD QUESTION
Front
Given the sequence 64, -16, 4, -1, what is the common ratio?
Back
r = -1/4.
4.
FLASHCARD QUESTION
Front
What is a recursive formula for a geometric sequence?
Back
A recursive formula defines each term based on the previous term, typically in the form a_n = r * a_(n-1), where r is the common ratio.
5.
FLASHCARD QUESTION
Front
What is the explicit formula for the nth term of a geometric sequence?
Back
The explicit formula is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.
6.
FLASHCARD QUESTION
Front
Identify the recursive formula for the sequence 2, -6, 18, -54.
Back
a_n = a_(n-1)(-3), a_1 = 2.
7.
FLASHCARD QUESTION
Front
What is the explicit formula for the nth term of a geometric sequence with a_4 = 108 and r = -2?
Back
a_n = -13.5 * (-2)^(n-1).
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