Arithmetic and geometric sequences
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•
Mathematics
•
10th Grade
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is an arithmetic sequence?
Back
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the 'common difference.' For example, in the sequence 2, 4, 6, 8, the common difference is 2.
Tags
CCSS.HSF.BF.A.2
2.
FLASHCARD QUESTION
Front
How do you find the nth term of an arithmetic sequence?
Back
The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.
Tags
CCSS.HSF.BF.A.2
3.
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.' For example, in the sequence 3, 6, 12, 24, the common ratio is 2.
Tags
CCSS.HSF.BF.A.2
4.
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.
Tags
CCSS.HSF.BF.A.2
5.
FLASHCARD QUESTION
Front
What is the common difference in the arithmetic sequence 5, 10, 15, 20?
Back
The common difference is 5, as each term increases by 5.
Tags
CCSS.HSF.BF.A.2
6.
FLASHCARD QUESTION
Front
What is the common ratio in the geometric sequence 2, 6, 18, 54?
Back
The common ratio is 3, as each term is multiplied by 3 to get the next term.
Tags
CCSS.HSF.BF.A.2
7.
FLASHCARD QUESTION
Front
Find the next term in the arithmetic sequence 4, 8, 12, 16.
Back
The next term is 20.
Tags
CCSS.HSF.BF.A.2
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