Algebra and Trigonometry, 5th Edition

Chapter 11 Summary and Review

Study Guide

Key Terms and Concepts	Examples
Section 11.1: Sequences and Series
An infinite sequence is a function having for its domain the set of positive integers $\{1,2,3,4,5,\dots \}$. A finite sequence is a function having for its domain a set of positive integers $\{1,2,3,4,5,\dots ,n\}$ for some positive integer n.	The first four terms of the sequence whose general term is given by $a_n=3n+2$ are $$\begin{array}{rcl}{a}_1\hfill & =\hfill & 3\cdot 1+2=5,\hfill \\ a_2\hfill & =\hfill & 3\cdot 2+2=8,\hfill \\ a_3\hfill & =\hfill & 3\cdot 3+2=11,\text{and}\hfill \\ a_4\hfill & =\hfill & 3\cdot 4+2=14.\hfill \end{array}$$
The sum of the terms of an infinite sequence is an infinite series. A partial sum is the sum of the first n terms. It is also called a finite series or the nth partial sum and is denoted $S_n$.	For the sequence above, $S_4=5+8+11+14$, or 38. We can denote this sum using ...