Problem 63
Question
What is an arithmetic sequence? Give an example with your explanation.
Step-by-Step Solution
Verified Answer
An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant. An example would be the sequence: 2, 5, 8, 11, 14, where the common difference is 3.
1Step 1: Definition
An arithmetic sequence, often known as an arithmetic progression in mathematical terms, is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is usually referred to as the 'common difference'.
2Step 2: Example
An example of an arithmetic sequence would be: 2, 5, 8, 11, 14... In this particular sequence, the common difference is 3 (5-2 = 3, 8-5 = 3, etc.). It's clear that the difference between any two consecutive terms in this sequence is always 3, hence making it an arithmetic sequence.
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