Algebra 1B Unit 1 Lesson 5 Flashcards
12 Questions
101 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

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,...}?

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

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

<p>161</p> Signup and view all the answers

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

<p>28</p> Signup and view all the answers

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

<p>-133</p> 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)?

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

What is the explicit formula represented by the given graph?

<p>f(n)=1−3(n−1)</p> Signup and view all the answers

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

<p>f(n)=3n+17</p> 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?

<p>an=22−10(n−1)</p> Signup and view all the answers

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

<p>a1=−4 and an=an−1+7</p> 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.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

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.

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser