Math vocabularies unit 1

Linear

Straight, continues

Improper fraction

General equation

Think parent equation

n also means

Nth term and U_n

sequence

List of numbers

Finite sequence

List of numbers with an ending term

Infinite sequence

List of numbers with no ending term

Arithmetic sequence

Sequence that changes with the addition or subtraction of a common difference

Geometric sequence

Sequence that changes with the multiplication or devision of a common ratio.

Series

Created when the terms of a sequence are added together

Recursive sequence

Neither arithmetic or geometric

Finite series

Fixed number of terms

Infinite series

Continues indefinitely

Sigma notation

A piece of information (upper limit) and n = read as an information provider. - can be in arithmetic or geometric equations.

Where is the upper limit on sigma

On top of the symbol

What does upper limit mean

Upper limit is told by sigma notiation - letting the reader know where the sequence stops.

N= means what (in sigma notation)

Telling you the starting term - what n equals for the equation that follows.

u_n = U₁ + (n-1)d

General term - for arithmetic sequences

How to find arithmetic sequences with only 2 terms given (not a list)

Use the equation of your 2 given terms to find a common difference or ratio, and then plug in the term you need to find.

U_n = u₁ r^n-1

General equation for what

Equations for sum or arithmetic sequences

S _n = n/2 (2n₁ + (n-1) d) ; S _n = n/2 (u₁ + u _n )

equations for the sum of a finite (ending term) geometric sequence

S _n = u ₁ (r ⁿ -1)/r-1 ; u₁ (1-r ⁿ )/1-r

Converging geometric sequence

A sequence where, as the index increases, the terms get arbitrarily close to a particular number, known as the limit. If for every positive number ε, there exists an integer N such that for all n > N, the absolute difference between the terms and the limit is less than ε. - meaning you will use s- infinity equation.

definition of a diverging geometric sequence

A sequence where the ratio between consecutive terms remains constant, and as the number of terms increases, the terms grow without bound (approach infinity) or decrease towards negative infinity. This occurs when the common ratio is greater than or equal to 1 or less than or equal to -1.