Arithmetic and Geometric Sequences - General Forms of a Sequence

Arithmetic and Geometric Sequence

Sequence - an ordered list of terms or elements






Arithmetic sequence formula: In an Arithmetic Sequence, the difference between one term and the next is a constant. AKA the Common Difference.
ARITHMETIC FORMULA:
an =a1 +(n-1)d:
n: term number
a(n): nth term
a: first term
r: common difference

Geometric Sequence Formula: In a Geometric Sequence, each term is found by multiplying the previous term by a constant. AKA Common Ratio.
GEOMETRIC FORMULA:
an=a1 + r (n - 1):
n: term number
a(n): nth term
a: first term
r: common ratio

Example:        2, 4, 8, 16, 32, 64...

This sequence has a factor of 2 between each number. Each term ( except the first term ) is found by multiplying the previous term by 2.

Finite sequence - Function with domain 1, 2, 3.

Infinite sequence - Function with domain 1, 2, 3, 4....

Series - Sum of a sequence

Explicit formula - Each domain is an answer not based on any values.

Recursive formula - Each domain is an answer based on a previous answer

Characteristics of a Graph

~~Characteristics of a Graph~~

Domain : Left and Right
Range : Up and Down

End Behavior :Describing the two ends of the graph. While X approaches negative infinity, Y approaches negative infinity. While X approaches positive infinity, Y approaches positive infinity and vice versa in another situation.          
                                          Left X -> (-∞)   y→-∞         y→-∞

                                                                   y→+∞   ( Describe 2 Ends)

                                         Right X -> (+∞)  y→-∞       y→-∞

                                                                   y→+∞
Absolute Max/Min: 1 Point highest/lowest on graph - A specific point on a graph

Local Max/Min: More than 1 point highest/lowest on graph

Interval of Increase: Section of a graph where the y-values increase (-∞, 0) 

Interval of Decrease: Section of a graph where the y-values decrease (0, +∞)

X Intercept: (a,0) crosses X axis

Y Intercept: (0,b) crosses Y axis

Symmetry: Even/Odd/Neither
Even: about the Y - Axis
Odd: rational symmetry about the origin
Neither: no symmetry

Asymptotes: Imaginary line that the graph gets closer and closer yet it never touches 

Function: Passes VLT ( Vertical Line Test) 

One to One: Passes VLT/ HLT ( Horizontal Line Test)