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

Selena Cowan

Selena Cowan

Answered

2022-01-25

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

Answer & Explanation

sjkuzy5

sjkuzy5

Expert

2022-01-26Added 11 answers

A sequence is called an arythmetic sequence if the difference of the term and the previous term is always the same.
For example, an+1an=constant(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 (41=3)
A sequence is called a geometric sequence if an+1an=constant 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 (a0)
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

Jaiden Conrad

Expert

2022-01-27Added 14 answers

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.

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