Arithmetic and Geometric Sequence and Series Flashcard

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•
Mathematics
•
11th - 12th Grade
•
Hard
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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 (d).
2.
FLASHCARD QUESTION
Front
How do you find the nth term of an arithmetic sequence?
Back
The nth term (a_n) of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.
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 (r).
4.
FLASHCARD QUESTION
Front
How do you find the nth term of a geometric sequence?
Back
The nth term (a_n) of a geometric sequence can be calculated using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.
5.
FLASHCARD QUESTION
Front
What is the formula for the sum of the first n terms of an arithmetic series?
Back
The sum (S_n) of the first n terms of an arithmetic series can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.
6.
FLASHCARD QUESTION
Front
What is the formula for the sum of an infinite geometric series?
Back
The sum (S) of an infinite geometric series exists if the absolute value of the common ratio (|r|) is less than 1, and is given by: S = a_1 / (1 - r), where a_1 is the first term.
7.
FLASHCARD QUESTION
Front
What is the common difference in an arithmetic sequence?
Back
The common difference (d) in an arithmetic sequence is the constant amount that each term increases or decreases by from the previous term.
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