Algebra 2 Honors: Series and Sequences Formulas

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.

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.