13. Arithmetic Sequences Explicit to Linear Functions
Flashcard
•
Mathematics
•
9th Grade
•
Practice Problem
•
Hard
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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.
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.
3.
FLASHCARD QUESTION
Front
What is the explicit formula for an arithmetic sequence?
Back
The explicit formula for an arithmetic sequence is a_n = a_1 + (n-1)d.
4.
FLASHCARD QUESTION
Front
What is a linear function?
Back
A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.
5.
FLASHCARD QUESTION
Front
How can you convert an arithmetic sequence to a linear function?
Back
You can convert an arithmetic sequence to a linear function by expressing the nth term of the sequence as a function of n, typically in the form f(n) = a_1 + (n-1)d.
6.
FLASHCARD QUESTION
Front
What is the common difference in an arithmetic sequence?
Back
The common difference is the constant amount that each term in the sequence increases or decreases by. It is calculated as d = a_n - a_(n-1).
7.
FLASHCARD QUESTION
Front
What does it mean to rewrite an explicit formula in function form?
Back
Rewriting an explicit formula in function form means expressing the formula in terms of a function notation, typically f(n) instead of a_n.
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