Questions and Answers
What is the formula for an arithmetic sequence?
What does the formula Sn = (n/2)(a1 + an) represent?
What is the formula for a geometric sequence?
What does the formula Sn = a1([1-rⁿ]/[1-r]) represent?
Signup and view all the answers
What does the recursive formula an = a∨n-1 + d describe?
Signup and view all the answers
What does the recursive formula an = a∨n-1 * r describe?
Signup and view all the answers
Study Notes
Arithmetic Sequence Formulas
-
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.
-
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
-
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.
-
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
-
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} ).
-
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
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
