Basic Technical Mathematics, 11th Edition

19.1 Arithmetic Sequences

• Arithmetic Sequence • Common Difference• Finite and Infinite Sequences • Sum of n Terms

A sequence of numbers may consist of numbers chosen in any way we may wish to select. This could include a random selection of numbers, although the sequences that are useful follow a pattern. We consider only those sequences that include real numbers or literal numbers that represent real numbers.

An arithmetic sequence (or arithmetic progression) is a set of numbers in which each number after the first can be obtained from the preceding one by adding to it a fixed number called the common difference. This definition can be expressed in terms of the recursion formula

$$a_n\hspace{0.17em}=\hspace{0.17em}{a}_{n\hspace{0.17em}-\hspace{0.17em}1}\hspace{0.17em}+\hspace{0.17em}d$$(19.1)

where $a_n$ is any term, $a_{n\hspace{0.17em}-\hspace{0.17em}1}$ is the preceding ...