Questions and Answers
What is an arithmetic sequence?
A sequence in which a fixed amount is added on to get the next term.
What is the common difference in an arithmetic sequence?
The fixed amount added on to get to the next term in an arithmetic sequence.
What is a sequence?
A set of numbers that follow a pattern, with a specific first number.
What is a term in terms of sequences?
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Which of the following is an arithmetic sequence?
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Find the common difference for the sequence: 1.05, 1.1, 1.15, 1.2,...
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What is the next term for the given arithmetic sequence: -3, -2.25, -1.5, -0.75,...?
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Find the common difference for the sequence shown: 56, 49, 42, 35,...
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Find the common difference of the arithmetic sequence shown: 1/4, 3/8, 1/2,...
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Which of the following equations could be used to solve for the tenth term of the following sequence: 15, 13, 11, 9,...?
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Find the 20th term of the following sequence: -6, -4, -2, 0,...
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If the first term of an arithmetic sequence is -3 and the fifteenth term is 53, what is the common difference of the sequence?
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Study Notes
Arithmetic Sequences
- An arithmetic sequence consists of numbers where a fixed amount is added to each term to obtain the next term.
- The common difference is the constant amount added to each term in an arithmetic sequence, defining the regularity of the sequence.
Key Concepts
- A sequence is a set of numbers arranged in a particular order, starting from a defined first number.
- Each value within a sequence is called a term, representing an individual number within that sequence.
Examples and Calculations
- Example of an arithmetic sequence: 0, 2, 4, 6, ... where the common difference is 2.
- For the sequence 1.05, 1.1, 1.15, 1.2, the common difference is 0.05.
- The next term in the sequence -3, -2.25, -1.5, -0.75, is 0, demonstrating that arithmetic sequences can include negative values.
- For the sequence 56, 49, 42, 35, the common difference is -7, illustrating a decrease in values.
Fractional Terms
- In the sequence comprising fractions 1/4, 3/8, 1/2, the common difference is 1/8, showcasing that arithmetic sequences can also involve fractions.
Term Calculation
- The equation A(10) = 15 + 9(-2) can be used to find the tenth term of the sequence 15, 13, 11, 9, indicating how to derive specific term values using a formula.
- The 20th term of the sequence -6, -4, -2, 0 is calculated to be 32, and demonstrates how to find far-term values in a sequence.
- If the first term of an arithmetic sequence is -3 and the fifteenth term is 53, the common difference can be determined to be 4, illustrating how to solve for common differences with given terms.
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Test your knowledge of arithmetic sequences with these flashcards. Each card introduces key terms and definitions crucial for understanding this fundamental concept in algebra. Perfect for students looking to reinforce their learning in Algebra 1.
