Honors Algebra II Sequences and Series

Recursive relation

an equation that uses a rule to generate the next term in the sequence from the previous term or terms

first term of a sequence can be written as

f(1)/a of 1/f(0)/a of 0

the next term can be written as

a of n+1/f(n+1)

the previous term can be written as

a of n-1/f(n-1)

Recursive formula of arithmetic sequence

a of 1 = start

a of n = a of n-1 + common difference

arithmetic sequence

a list of numbers with a common increase or decrease(common difference)

arithmetic sequences represent

linear relationships where the common difference is the slope(and the zeroeth term is the y intercept)

Arithmetic recursive formula

a of n = a of 1 + d(n-1)

geometric sequence

a list of numbers with a common increase or decrease known as the common ratio

A geometric sequence represents an

exponential relationship where the common ratio represents the growth/decay factor

recursive geometric formula

a of 1 = first term

a of n = r x a of n-1

explicit geometric formula

a of n = a of 1( r )^n-1

Geometric series formula

s of n = a of 1 - a of 1( r )^n/ 1-r

Geometric series for growth

r = 1 + rate

geometric series for decay

r = 1-r

geometric series for compounded growth

r = (1+ rate/# of times compounded)

To use sigma notation to represent a series,

1. write the explicit formula

2. find n values for the first and last terms