Discrete Math Notes:
Chapter 7: Recursion
7.1 Sequences
Sequence, a special type of function in which the domain is a set of consecutive integers.
Term, A value in gk
Index, k would be considered the index of gk
finite sequence, a sequence with a finite domain
initial index, a finite sequence
infinite sequence, a sequence with an infinite domain
explicit formula, a sequence can be specified
increasing, increasing if for every two consecutive indices, k and k + 1, in the domain, ak < ak+1.
non-decreasing, if for every two consecutive indices, k and k + 1, in the domain, ak ak+1
decreasing, if for every two consecutive indices, k and k + 1, in the domain, ak > ak+1.
non-increasing, if for every two consecutive indices, k and k + 1, in the domain, ak ak+1.
geometric sequence, a sequence of real numbers where each term after the initial term
common ratio, the initial term is found by taking the previous term and multiplying by a fixed number
arithmetic sequence, a sequence of real numbers where each term after the initial term is found by taking the previous term and adding a fixed number
Overview:
A sequence is a type of function whose domain consists of a set of successive integers. For example, a
infinite sequence is a sequence with an unlimited domain. The indices in an endless sequence go to infinity in the positive direction. A geometric sequence is a set of real numbers in which each phrase after the first is determined by multiplying the previous term by a constant termed the common ratio.
numbers in which each term after the first is found by taking the preceding term and multiplying it by a constant called the common difference. There are two types of arithmetic seguences: finite and infin