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Chapter 10: Problem 73

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

Short Answer

Expert verified
A sequence is a set of terms (numbers), arranged in order, which may be infinite or finite. An example is 1, 3, 5, 7, 9 which shows an arithmetic sequence with a common difference of 2.

Step by step solution

01

Define a Sequence

A sequence is a set of numbers, also known as terms, that are arranged in a specific order. The sequence may be infinite (having an infinite number of terms) or finite (having a finite number of terms). Each term in a sequence is designated by a particular index.
02

Explaining the General Structure of a Sequence

The general structure of a sequence may be represented as \(a_1, a_2, a_3, a_4, ..., a_n\) where \(a_n\) is the nth term of the sequence.
03

Provide an Example

An example of a sequence is the arithmetic sequence 1, 3, 5, 7, 9. Here, each subsequent number (term) is obtained by adding 2 to the previous number. In general, the nth term (denoted by \(a_n\)) in an arithmetic sequence is given by the formula: \(a_n = a_1 + (n-1) * d\) where \(d\) is the common difference (which is 2 in this example), \(n\) is the position of the term in the sequence, and \(a_1\) is the first term.

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