an represents the nth term of the sequence. A simple way to generate a sequence is to start with a number a, and add to it a fixed constant d, over and over again. An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. For example, the ratio between the first and the second term in the harmonic sequence is $\frac$ so the difference is again not the same and hence the harmonic sequence is NOT an arithmetic sequence. The first term is represented by a1, the second term is represented by a2, and so on. SOLUTION: An arithmetic sequence is a numerical pattern that increases or decreases at a constant rate called the common difference. For example, the Fibonacci sequence $1,1,2,3,5,8.$ is neither.Ī geometric sequence is one that has a common ratio between its elements. Not all sequences are geometric or arithmetic. In an arithmetic sequence, the difference between consecutive terms is always the same. The sequence you gave is called the Harmonic sequence. Sequences with such patterns are called arithmetic sequences.
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