Section 9.1

Series and Sequences 

A sequence can be known as A_{n. The first term of the sequence is known as} a_{1,  . A sequence can also be a function but its domain has to be natural numbers.}

Recursive Sequence

A recursive sequence is a pattern that can be calculated in a finite  number of steps.  A recursive formula has two parts: the starting value A₁and the the recursion equation,  A_k a function of A<sub>k-1.

Ex.</sub>

A_k +1= A_k-5

Next term=Now term-5

Ex.

A₁= 4

A_k+1=A_k-5

Defined as the initial conditions for a recursive formula.

Ex.

Explicit Sequence

An explicit formula allows you to find the any nth term within the sequence. There is no clear cut formula for finding an explicit formula. Explicit formulas are found by reasoning and using the patterns within the sequence to find the nth term.

Ex.

Additional Info:http://www.khanacademy.org/math/trigonometry/seq_induction/seq_and_series/v/arithmetic-sequences