Algebra 1B Unit 1 Lesson 5 Flashcards

Questions and Answers

What is the common difference between the terms in the sequence {17, 11, 5, -1, -7...}?

-6

What is the recursive formula for the sequence where the first term is 9 and each value is 4 more than the previous value?

a1=9 and an=an−1+4

Which recursive formula represents the sequence with initial terms a1=10, a2=6, a3=2, a4=−2?

a1=10 and an=an−1−4

What is the recursive formula for the sequence {−4,−1,2,5,...}?

f(1)=−4 and f(n+1)=f(n)+3 Signup and view all the answers

What is the 55th term of the sequence defined by the explicit formula an=−1+3(n−1)?

161 Signup and view all the answers

What is the 21st term of the sequence given by an=−2+32(n−1)?

28 Signup and view all the answers

What is the 30th term of the sequence defined by an=12−5(n−1)?

-133 Signup and view all the answers

Which explicit formula represents the arithmetic sequence given by the points (1, -2), (2, 3), (3, 8), (4, 13)?

an=−2+5(n−1) Signup and view all the answers

What is the explicit formula represented by the given graph?

f(n)=1−3(n−1) Signup and view all the answers

Which function correctly represents the arithmetic sequence {20, 23, 26, 29, 32}?

f(n)=3n+17 Signup and view all the answers

What is the explicit formula for the sequence with an initial term a1=22 and recursive formula an=an−1−10?

an=22−10(n−1) Signup and view all the answers

What is the recursive formula for the sequence defined by the explicit formula an=−4+7(n−1)?

a1=−4 and an=an−1+7 Signup and view all the answers

Study Notes

Sequences and Formulas

The common difference in the sequence {17, 11, 5, -1, -7} is -6, indicating a consistent decrease between terms.
A sequence starting with 9, where each term increases by 4, has a recursive formula: a1 = 9 and an = an-1 + 4.
For the sequence a1 = 10, a2 = 6, a3 = 2, a4 = -2, the recursive formula is a1 = 10 and an = an-1 - 4, demonstrating a consistent decrease.
The sequence {-4, -1, 2, 5, ...} has a recursive formula of f(1) = -4 and f(n+1) = f(n) + 3, indicating a consistent increase.

Explicit Formulas and Terms

The explicit formula an = -1 + 3(n - 1) yields a 55th term of 161, calculated by substituting n = 55 in the formula.
For the formula an = -2 + 32(n - 1), the 21st term is calculated as 28.
The term derived from the formula an = 12 - 5(n - 1) for n = 30 is -133, indicating a decrease in value as n increases.

Graphs and Function Representation

The explicit formula for the arithmetic sequence represented in the table (1, -2), (2, 3), (3, 8), (4, 13) is an = -2 + 5(n - 1), indicating a slope of 5.
The graph implies an explicit formula f(n) = 1 - 3(n - 1) showcasing a linear decrease influenced by the coefficient of n.

Additional Functions and Transitions

The arithmetic sequence {20, 23, 26, 29, 32} can be represented as f(n) = 3n + 17, reflecting a steady increase of 3 for each subsequent term.
For a sequence starting at a1 = 22 with the recursive definition an = an-1 - 10, the equivalent explicit formula is an = 22 - 10(n - 1).
An explicit formula an = -4 + 7(n - 1) corresponds to the recursive formula a1 = -4 and an = an-1 + 7, demonstrating an additive relationship among terms.

Description

Test your knowledge of sequences and their properties with these flashcards from Algebra 1B Unit 1 Lesson 5. Each card covers topics such as common differences and recursive formulas. Enhance your understanding of algebraic sequences through targeted practice.