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Questions and Answers
What is the formula for an arithmetic sequence?
What is the formula for an arithmetic sequence?
What does the formula Sn = (n/2)(a1 + an) represent?
What does the formula Sn = (n/2)(a1 + an) represent?
What is the formula for a geometric sequence?
What is the formula for a geometric sequence?
What does the formula Sn = a1([1-rⁿ]/[1-r]) represent?
What does the formula Sn = a1([1-rⁿ]/[1-r]) represent?
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What does the recursive formula an = a∨n-1 + d describe?
What does the recursive formula an = a∨n-1 + d describe?
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What does the recursive formula an = a∨n-1 * r describe?
What does the recursive formula an = a∨n-1 * r describe?
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Study Notes
Arithmetic Sequence Formulas
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Nth Term Formula: ( a_n = a_1 + d(n-1) )
- Represents the output for the nth term.
- ( a_1 ) is the first term, ( d ) is the common difference, ( n ) is the term position.
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Summation Formula: ( S_n = \frac{n}{2}(a_1 + a_n) )
- Calculates the sum of the first ( n ) terms of an arithmetic series.
- ( S_n ) is the total sum, ( n ) is the number of terms, ( a_1 ) is the first term, and ( a_n ) is the last term.
Geometric Sequence Formulas
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Nth Term Formula: ( a_n = a_1 r^{n-1} )
- Defines the output for the nth term.
- ( a_1 ) is the first term, ( r ) is the common ratio, ( n ) indicates the term number.
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Summation Formula: ( S_n = a_1 \left(\frac{1 - r^n}{1 - r}\right) )
- Used for finding the sum of the first ( n ) terms of a geometric series.
- ( S_n ) denotes the total sum, ( a_1 ) is the first term, ( r ) is the common ratio, and ( n ) signifies the number of terms.
Recursive Formulas
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Recursive Arithmetic Formula: ( a_n = a_{n-1} + d )
- Expresses the nth term based on the previous term.
- Adds the common difference ( d ) to the previous term ( a_{n-1} ).
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Recursive Geometric Formula: ( a_n = a_{n-1} \times r )
- Indicates how to find the nth term using the preceding term.
- Multiplies the previous term ( a_{n-1} ) by the common ratio ( r ).
Studying That Suits You
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Description
Test your knowledge of sequences and series formulas with these flashcards. Each card presents a specific formula and its definition, including both arithmetic and geometric sequences. Perfect for students who want to reinforce their understanding and application of these mathematical concepts.
