Algebra 2/Trig H: Unit 8 Series and Sequences

Questions and Answers

What is the recursive formula for an arithmetic sequence?

f(n) = f(n-1) * r

a1(1-r^n)/(1-r)

f(n) = f(n-1) + d (correct)

n(a1 + an)/2

What is the recursive formula for a geometric sequence?

an=a1(r)^(n-1)

f(n) = f(n-1) * r (correct)

a1+(n-1)d

f(n) = f(n-1) + d

What is the formula for the arithmetic sum?

n(a1 + an)/2

What is the formula for the geometric sum?

a1(1-r^n)/(1-r) Signup and view all the answers

What is the formula for an arithmetic sequence?

a1+(n-1)d Signup and view all the answers

What is the formula for a geometric sequence?

an=a1(r)^(n-1) Signup and view all the answers

How do you find the common difference in an arithmetic sequence?

(value y - value x)/(term y - term x) Signup and view all the answers

How do you find the common ratio in a geometric sequence?

(term x - term y) √(x value/y value) Signup and view all the answers

Study Notes

Arithmetic and Geometric Sequences

Arithmetic Sequence Recursive Formula: Defined as ( f(n) = f(n-1) + d ) or ( A_n = A_{n-1} + d ), where ( d ) is the common difference between terms.
Geometric Sequence Recursive Formula: Expressed as ( f(n) = f(n-1) \times r ) or ( A_n = A_{n-1} \times r ), where ( r ) is the common ratio.

Sums of Sequences

Arithmetic Sum Formula: Calculated using ( S_n = \frac{n(a_1 + a_n)}{2} ), where ( S_n ) is the sum of the first ( n ) terms, ( a_1 ) is the first term, and ( a_n ) is the last term.
Geometric Sum Formula: Given by ( S_n = \frac{a_1(1 - r^n)}{1 - r} ) for ( r \neq 1 ), where ( S_n ) represents the sum of the first ( n ) terms of a geometric series.

Formulas for General Terms

Arithmetic Sequence General Formula: Expressed as ( a_n = a_1 + (n-1)d ), indicating the ( n^{th} ) term can be found by adding the first term to ( (n-1) ) times the common difference.
Geometric Sequence General Formula: Written as ( a_n = a_1(r)^{n-1} ), which allows determination of the ( n^{th} ) term by using the first term multiplied by the common ratio raised to the power of ( (n-1) ).

Finding Sequence Properties

Common Difference: Determined by the formula ( \frac{\text{value}_y - \text{value}_x}{\text{term}_y - \text{term}_x} ), which calculates how much each term increases or decreases.
Common Ratio: Found using ( \frac{\text{term}_y}{\text{term}_x} ) for ( \sqrt{x \text{ value} / y \text{ value}} ), indicating the factor by which each successive term is multiplied.

Description

Test your knowledge on series and sequences formulas in Algebra 2/Trig H with these flashcards. This quiz covers key recursive formulas and sums for both arithmetic and geometric sequences. Perfect for students looking to reinforce their understanding of this crucial mathematical topic.