Math Chapter 9 Vocab

finite

A sequence is a ___ sequence if the domain of the function consists of the first n positive integers.

arithmetic

A sequence is an ___ sequence if the first differences are all the same nonzero number.

geometric;common

A sequence is called a ___ sequence if the ratios between consecutive terms are the same. This ratio is called the ___ ratio.

arithmetic;common

A sequence is called an ___ sequence if the differences between two consecutive terms are the same. This difference is called the ___ difference.

infinite sequence

An ___ ___ is a function whose domain is the set of positive integers.

index;upper;lower

For the sum (sigma notation here), i is called the ___ of summation, n is the ___ limit of summation, and 1 is the ___ limit of summation.

factorial

If n is a positive integer, n ___ is defined as n! = 1 x 2 x 3 ... (n-1) x n.

second

If the ___ differences of a sequence are all the same nonzero number, the sequence has a perfect quadratic model.

recursively

If you are given one or more of the first few terms of a sequence, and all other terms of the sequence are defined using previous terms, then the sequence is said to be defined ___.

nth partial sum

The ___ ___ ___ of a sequence is the sum of the first n terms of the sequence.

first

The ___ differences of a sequence are found by subtracting consecutive terms.

mathematical induction

The first step in proving a formula by ___ ___ is to show that the formula is true when n=1.

sum;finite arithmetic sequence

The formula Sn=n/2(a1+an) can be used to find the sum of the first n terms of an arithmetic sequence, called the ___ of a ___ ___ ___.

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

The formula for the sum of a finite geometric sequence is given by ___.

S=a1/(1-r)

The formula for the sum of an infinite geometric sequence is given by ___.

terms

The function values a1, a2,... are called the ___ of a sequence.

summation notation

The notation used to represent the sum of the terms of a finite sequence is ___ ___ or sigma notation.

an=a1r^n-1

The nth term of a geometric sequence has the form ___.

an=dn+c

The nth term of an arithmetic sequence has the form ___.

series

The sum of the terms of a finite or infinite sequence is called a ___.

geometric series

The sum of the terms of an infinite geometric sequence is called a ___ ___.