Lesson 11 (1 - 3) Sequences and Summation Notation/Arithmetic and Geometric Sequences

Factorial Notation

"n factorial" = n! = 1*2*3*4*5*6 ...*(n-1)*n

"n"th Term in Arithmetic Sequence

"n"th Term = a[1] + (n-1)d

Convergent

A geometric series that approaches a certain sum

Divergent

A geometric series that does not have a certain sum, and goes to infinity

Recursive Formula

A rule in which one or more previous terms are used to generate the next term

Explicit Formula

A rule in which the (n)th term is defined as a function of "n"

Arithmetic Sequence

A sequence in which the difference between any 2 terms is constant

Geometric Sequence

A sequence in which the ration between any two terms is constant

Summation Notations

A way to represent the sum of the finite sequence

Sequences

Implies and order or pattern

Fibonacci Sequence

Next number in sequence is the sum of the previous two number in the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610... Ration of 1:1.618 (next number/last number)

(Finite) Geometric Sequence

The sum of a (finite) geometric sequence

Arithmetic Series

The sum of a finite arithmetic sequence

Finite Series/"n"th Partcial

The sum of the terms in a infinite sequence

Series

The sum of the terms in a sequence

Geometric Sequence Formula

Used to find any "n"th term in a geometric sequence

Common Difference

Variable = d The numeric difference between 2 terms in an arithmetic Sequence

Common Ration

Variable = r The numerical ratio between and two terms