pre calculus Sequences

arithmetic sequences

a sequence in which each term after the first, a, is equal to the sum of the previous term and a common difference, d

arithmetic equation

an = a1 + (n-1)d

geometric sequence

a sequence in which each term after the first, a1, is the product of the preceding term and a common ration, r

geometric equation

an = a1r^n-1

explicit formula

formulas that describe the nth term in terms of n

recursive formula

each term is formulated from one or more previous terms

initial conditions

where to start a1

parts of recursive formula

initial condition and recurrence relation

recurrence relation

expresses each term of the sequence in terms of previous terms in the sequence an= f(an-1)