Questions and Answers
What is the formula for the term of an arithmetic sequence?
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What are the formulas for the sum of an arithmetic series?
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What is the formula for the term of a geometric sequence?
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What is the formula for the sum of finite geometric series?
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What is the ratio for a geometric infinite divergent series and its possible sum?
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What is the ratio for a geometric infinite convergent series and its possible sum?
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What is the formula for the sum of infinite geometric series and the ratio restriction?
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How do you find the number of terms given sigma notation?
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Study Notes
Arithmetic Sequences
- The formula for finding any term in an arithmetic sequence is: ( a_n = a_1 + (n-1)d ) where ( a_1 ) is the first term, ( d ) is the common difference, and ( n ) is the term number.
Sum of Arithmetic Series
- The formula for the sum of the first ( n ) terms of an arithmetic series is: ( S_n = \frac{n}{2} (a_1 + a_n) ) or ( S_n = \frac{n}{2} \cdot d \cdot (n-1) ).
Geometric Sequences
- The formula for finding any term in a geometric sequence is: ( a_n = a_1 \cdot r^{(n-1)} ) where ( a_1 ) is the first term and ( r ) is the common ratio.
Finite Geometric Series
- The formula for the sum of a finite geometric series is: ( S_n = \frac{a_1(1 - r^n)}{1 - r} ) for ( r \neq 1 ).
Infinite Geometric Series (Divergent)
- For an infinite geometric series, if the absolute value of the ratio ( r ) is greater than 1 (|r| > 1), the series diverges and has no finite sum.
Infinite Geometric Series (Convergent)
- An infinite geometric series converges if the ratio ( r ) falls within the range -1 < r < 1. The sum exists and varies within this constraint.
Sum of Infinite Geometric Series
- The formula for the sum of an infinite geometric series, valid under the condition -1 < r < 1, is: ( S = \frac{a_1}{1 - r} ) where ( a_1 ) is the first term.
Sigma Notation and Number of Terms
- To determine the number of terms represented by a sigma notation, use the formula ( (n - n_1) + 1 = ) number of terms, where ( n ) is the upper limit and ( n_1 ) is the lower limit.
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Description
Test your knowledge on key formulas related to series and sequences in Algebra 2 Honors. This quiz covers arithmetic and geometric sequences, as well as the sums of these series. Perfect for reviewing vital concepts before exams.
