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 $\{1,\text{}2,\text{}3,\text{}4,\text{}5,\dots \}$. A finite sequence is a function having for its domain a set of positive integers $\{1,\text{}2,\text{}3,\text{}4,\text{}5,\dots ,n\}$ for some positive integer n. 
The first four terms of the sequence whose general term is given by ${a}_{n}=3n+2$ are $$\begin{array}{rcl}{a}_{1}\hfill & =\hfill & 3\cdot 1+2=5,\hfill \\ {a}_{2}\hfill & =\hfill & 3\cdot 2+2=8,\hfill \\ {a}_{3}\hfill & =\hfill & 3\cdot 3+2=11,\text{\hspace{1em}}\text{and}\hfill \\ {a}_{4}\hfill & =\hfill & 3\cdot 4+2=14.\hfill \end{array}$$ 
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 ... 
Get Algebra and Trigonometry, 5th Edition now with the O’Reilly learning platform.
O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.