Exam Three: Sequences and Summations

Sequence

A function with domain that is a subset of the set of integers

Geometric Sequence

A sequence of the form a, ar, ar², …, where a and r are real numbers

Arithmetic Sequence

A sequence of the form a, a + d, a + 2d, …, where a and d are real numbers

Recurrence Relation

An equation that expresses the nth term a_n of a sequence in terms of one or more of the previous terms of the sequence for all integers n greater than a particular integer

Closed-Form Solution

When we say that we have solved the recurrence relation together with the initial conditions when we find an explicit formula, this is for the terms of the sequence

Method: Solution by Iteration

When you repeatedly use the recurrence relation??

Summation

Index of Summation

Arithmetic Properties of Summation

Closed-Form Solutions (Table 2)