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