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Questions and Answers
What is the common difference between the terms in the sequence {17, 11, 5, -1, -7...}?
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?
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?
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,...}?
What is the recursive formula for the sequence {−4,−1,2,5,...}?
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What is the 55th term of the sequence defined by the explicit formula an=−1+3(n−1)?
What is the 55th term of the sequence defined by the explicit formula an=−1+3(n−1)?
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What is the 21st term of the sequence given by an=−2+32(n−1)?
What is the 21st term of the sequence given by an=−2+32(n−1)?
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What is the 30th term of the sequence defined by an=12−5(n−1)?
What is the 30th term of the sequence defined by an=12−5(n−1)?
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Which explicit formula represents the arithmetic sequence given by the points (1, -2), (2, 3), (3, 8), (4, 13)?
Which explicit formula represents the arithmetic sequence given by the points (1, -2), (2, 3), (3, 8), (4, 13)?
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What is the explicit formula represented by the given graph?
What is the explicit formula represented by the given graph?
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Which function correctly represents the arithmetic sequence {20, 23, 26, 29, 32}?
Which function correctly represents the arithmetic sequence {20, 23, 26, 29, 32}?
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What is the explicit formula for the sequence with an initial term a1=22 and recursive formula an=an−1−10?
What is the explicit formula for the sequence with an initial term a1=22 and recursive formula an=an−1−10?
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What is the recursive formula for the sequence defined by the explicit formula an=−4+7(n−1)?
What is the recursive formula for the sequence defined by the explicit formula an=−4+7(n−1)?
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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
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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.
