General Forms of a Sequence

General Forms Of A Sequence:

~Sequence: series (list) of numbers

~Arithmetic:  sequence of numbers such that the difference between the consecutive terms is constant.
            
             -example-  5,7,9,11,13,15... is an arithmetic sequence with a                               difference of 2.

             -formula-  a_n=  a₁+(n-1)d                    d=a_n-a_n-1

                                            _{d= common difference}

~Geometric: sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
             -example-  2,6,18,54... is a geometric sequence with a common                      ratio of 3.

             -formula-  a_n=a_{1 x} r^n-1                                  r= a_n ÷ a_n-1

                                                      _{r= common ratio} 

Characteristics of Graphs

                                               Characteristics of Graphs:
Domain: x-values

Range: y-values

End Behavior: description of what happens on both ends

Absolute Max/Min: 1 highest/lowest point

Local Max/Min: more than 1 highest/lowest point

Interval of Increase: what happens to a graph(y values) as you move along x-axis if y values are increasing 

Interval of Decrease: what happens to a graph as you move along x-axis if y values are decreasing

X Intercept: (a,o)

Y Intercept: (o,b)

Symmetry: even: symmetric about y-axis
                   odd: symmetric about origin
                   Neither: none

Even/Odd/Neither:  even: symmetric about y-axis
                                 odd: symmetric about origin
                                 Neither: none

Asymptotes: imaginary line that a graph gets closer and closer to but never touch

Function: describing what happens to a graph (function)

One to One: passes both vertical and horizontal line test

                                                          example of a functon (above)