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Chapter 11: Problem 72

What is an arithmetic sequence? Give an example with your explanation.

Short Answer

Expert verified
An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the preceding term. For example, in the sequence 2, 4, 6, 8, 10,... the constant difference is 2.

Step by step solution

01

Definition of an Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which any term after the first is obtained by adding a constant difference to the preceding term. This constant difference is often written as 'd'.
02

Explain constant difference

\(d\) can be found by subtracting the first term from the second term in the sequence. For instance, if the sequence is denoted as \( a_1, a_2, a_3, ..., a_n \), then \(d = a_2 - a_1\). This difference remains the same throughout the sequence.
03

Provide an example

A common example of an arithmetic sequence is 2, 4, 6, 8, 10,... Here, the constant difference \(d\) is 2, as each term is 2 greater than the previous term.

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