Chapter 10 Sequence and Series

Recursions

formula is determined by one or more of the previous terms

Summation notation

n= (top # - bottom #)+1 a1=plug bottom # into equation an=plug top # into equation r=# with exponent (ex: (4)², r=4

Iterations

process of repeatedly composing functions x₀=6, f(x)=-3x+8 x₁=-3(6)+8=-10 x₂=-3(-10)+8=38

Infinite series formula

r has to be less than one or else it doesn't have a sum

Arithmetic sequence

when a pattern is added by the same number. It has a common difference "d" Ex: 3, 7, 11, 15 d=4

Geometric sequence

when a pattern is multiplied by the same number. Has a common ratio "r" Ex: 1, 2, 4, 8, 16 r=2

Geometric mean formula

√xy

Arithmetic mean formula

(x+y)/2