Sequence

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Arithmetic

Series

Infinite

Geometirc

Definiton

Sigma

Arithmetic

Recursive

Explicit

Geometric

Sequence

An ordered list of numbers

how to generate the next term (Un+1, Un-1)

Explicit Rule

General Term

common difference = d

Explicit Rule

Recursive Definition

Un+1 = Un + d

Number upon ∑: Ending term

Un = Un-1 +d

common difference = constant ratio : r = U2/U1 = U3/U2 ... = Un+1/Un

Number under ∑: starting term

General Term

Formula beside ∑: Rule to generate the terms we are adding

Un = U1 + (n-1)d

Un=U1r^(n-1)

S∞ = U1 / (1-r ), ∣r∣<1

Recursive Definition

Un = rUn-1 OR Un+1 = rUn

Pattern

Linear

Quadratic

first common difference between consecutive terms

A sequence with terms that tend to
Zero are called convergent

Involve square numbers

Un = An + b

a=second difference/2

Recursive Definition

Un+1 = Un+a

Series is a sum of terms of sequence

Sn = U1(1-r^n) / 1-4 = U1(r^n-1) / r-1