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Chapter 14: Problem 61

What is a sequence? Give an example with your description.

Short Answer

Expert verified
A sequence is a list of numbers, functions, or other mathematical objects where the order matters and repetition is allowed. For example, the sequence of natural numbers \(a_n = n\), for \(n = 1, 2, 3, ...\) is an infinite sequence where each term is one unit greater than the previous term.

Step by step solution

01

Definition of a sequence

Start by defining what a sequence is. A sequence is a list of numbers, functions, or other mathematical objects where the order matters and repetition is allowed. They can be finite or infinite.
02

Detailed Explanation

Each of these numbers, functions, or objects in the sequence is called a term or an element of the sequence. They can follow a specific mathematical formula, a rule, or no clearly dominant pattern at all.
03

Example of a sequence

Provide an example to understand this better. For example, the sequence of natural numbers is an infinite sequence where each term is one unit greater than the previous term. If we denote this sequence as \(a_n\), then it can be represented as \(a_n = n\), for \(n = 1, 2, 3, ...\)
04

Wrap up

So a sequence is essentially a list of mathematical objects where each object has its own specific position. Sequences can be finite or infinite

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\sum_{i=1}^{4} 3 i+\sum_{i=1}^{4} 4 i=\sum_{i=1}^{4} 7 i$$

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