
Sequences, series, and probability
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
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.
2.
FLASHCARD QUESTION
Front
What is the formula for the sum of an infinite geometric series?
Back
The sum S of an infinite geometric series can be calculated using the formula S = a / (1 - r), where a is the first term and r is the common ratio (|r| < 1).
3.
FLASHCARD QUESTION
Front
What is the common ratio in the geometric sequence: 512, 256, 128, ...?
Back
The common ratio is 1/2, as each term is half of the previous term.
4.
FLASHCARD QUESTION
Front
How do you find the sum of a finite geometric series?
Back
The sum S of a finite geometric series can be calculated using the formula S_n = a(1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms.
5.
FLASHCARD QUESTION
Front
What is a common difference in an arithmetic sequence?
Back
The common difference is the constant amount that each term in an arithmetic sequence increases or decreases by, calculated as the difference between any two consecutive terms.
6.
FLASHCARD QUESTION
Front
Identify the common difference in the sequence: 97, 86, 75, 64, ...
Back
The common difference is -11.
7.
FLASHCARD QUESTION
Front
What is the explicit formula for an arithmetic sequence?
Back
The explicit formula for an arithmetic sequence is given by 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.
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