Precalculus Unit 5 Exam ☹️

What operations happen in an arithmetic sequence?

Add or subtract (linear)

What operations happen in a geometric sequence

Multiply or divide (exponential)

“A_n=2n+3” What is the constant rate, and what letter is represented?

2, or D

“A_n=2n+3” What kind of sequence is this? What form is it written in?

Arithmetic; explicit

“A_1=1; A_n = A_n-1+3”

What is d? What kind of equation is this? What form is this? How do you turn this into explicit

3=d, constant rate

Arithmetic

Recursive

Take d • n + or - what ever is need to make d • n = A_1

Recursive Geometric

A_n = A_n-1 • r

What is r in geometric sequences?

The ratio or constant rate

Explicit geometric

A_n=A_1( r )^n-1

Required set up for Recurrence Relation

F_n=AF_n-1+BF_n-2

What form do you turn the recurrence relation into first

X²+AX+B=0

What do you do when you have the recurrence relation as a quadratic?

Solve for roots: X_1 and X_2

Equation for real roots characteristic polynomial

F_n=ax_1^n+bx_2^n

What should your final answer be after solving a characteristic polynomial system?

Explicit form

S_n=nΣ