6.3 Arithmetic & Geometric Sequences and Series
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Wayground Content
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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).
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 (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.
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 (r).
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 (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.
Tags
CCSS.HSF.BF.A.2
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_1 is the first term and a_n is the nth term.
6.
FLASHCARD QUESTION
Front
What is the formula for the sum of the first n terms of a geometric series?
Back
The sum (S_n) of the first n terms of a geometric series can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), for r ≠ 1.
Tags
CCSS.HSA.SSE.B.4
7.
FLASHCARD QUESTION
Front
If a_15 = 108 and d = 7, what is a_1?
Back
a_1 = 10.
Tags
CCSS.HSF.BF.A.2
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