What's the difference between arithmetic, geometric, harmonic and Fabonacci sequences?

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What&#039;s the difference between arithmetic, geometric, harmonic and Fabonacci sequences?

sjkuzy5 · Accepted Answer

A sequence is called an arythmetic sequence if the difference of the term and the previous term is always the same.   For example, an+1−an=constan⁡t(d)  the constant difference, generally denoted by (d) is called the common difference.  Ex. 1,4,7,10,… is an arythmetic sequence, whose first term is 1 and the common difference is equal to (4−1=3)  A sequence is called a geometric sequence if an+1an=constan⁡t for all n.  Ex. the sequence 4,12,36,… is a geometric sequence, because 124=3612=…=3, which is constant.  A sequence is harmonic when each term is harmonic mean of the neighboring terms.   For example, 1a,1a+d,1a+2d,…, here (a≠0)  Ex. 1,12,13,14,…  here, a=1 (first term)  d=1 (common difference)  The Fibonacci sequence starts like this: 0,1,1,2,3,5,8,13,21,…  Each number is the sum of the two numbers that precede it.

Jaiden Conrad · Accepted Answer

Arithmetic sequence is a sequence where the difference between two consecutive terms is constant while a geometric sequence is a sequence where the ratio between two consecutive terms is constant.

What's the difference between arithmetic, geometric, harmonic and Fabonacci sequences?

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