Math and Arithmetic
Algebra
The Difference Between

# What is the difference between a geometric sequence and arithmetic sequence?

567 ###### 2011-03-04 17:01:54

Goemetric sequence :

A sequence is a goemetric sequence if an/an-1is the same non-zero number for all natural numbers greater than 1.

Arithmetic sequence :

A sequence {an} is an arithmetic sequence if an-an-1 is the same number for all natural numbers greater than 1.

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## Related Questions In an arithmetic sequence the same number (positive or negative) is added to each term to get to the next term.In a geometric sequence the same number (positive or negative) is multiplied into each term to get to the next term.A geometric sequence uses multiplicative and divisive formulas while an arithmetic uses additive and subtractive formulas. The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers". To check whether it is an arithmetic sequence, verify whether the difference between two consecutive numbers is always the same.To check whether it is a geometric sequence, verify whether the ratio between two consecutive numbers is always the same. The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers". An arithmetic sequence is a list of numbers which follow a rule. A series is the sum of a sequence of numbers. No, the Fibonacci sequence is not an arithmetic because the difference between consecutive terms is not constant You take the difference between the second and first numbers.Then take the difference between the third and second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Take the difference between the fourth and third second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Keep checking until you think the differences are all the same.That being the case it is an arithmetic sequence.If you have a position to value rule that is linear then it is an arithmetic sequence. It is an arithmetic sequence if you can establish that the difference between any term in the sequence and the one before it has a constant value.  The sequence is arithmetic if the difference between every two consecutive terms is always the same. The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers". The common difference is the difference between two numbers in an arithmetic sequence. Yes, with a difference of zero between terms. It is also a geometric series, with a ratio of 1 in each case. You can find the differences between arithmetic and geometric mean in the following link: "Calculation of the geometric mean of two numbers".  An arithmetic sequence is a line-up of numbers in which the DIFFERENCE between any two next-door neighbors is always the same. An arithmetic series is the sequence of partial sums of an arithmetic sequence. That is, if A = {a, a+d, a+2d, ..., a+(n-1)d, ... } then the terms of the arithmetic series, S(n), are the sums of the first n terms and S(n) = n/2*[2a + (n-1)d]. Arithmetic series can never converge.A geometric series is the sequence of partial sums of a geometric sequence. That is, if G = {a, ar, ar^2, ..., ar^(n-1), ... } then the terms of the geometric series, T(n), are the sums of the first n terms and T(n) = a*(1 - r^n)/(1 - r). If |r| It is the difference between a term (other than the second) and its predecessor.  Succession of numbers of which one number is designated as the first, other as the second, another as the third and so on gives rise to what is called a sequence. Sequences have wide applications. In this lesson we shall discuss particular types of sequences called arithmetic sequence, geometric sequence and also find arithmetic mean (A.M), geometric mean (G.M) between two given numbers. We will also establish the relation between A.M and G.M  The sequence in the question is NOT an arithmetic sequence. In an arithmetic sequence the difference between each term and its predecessor (the term immediately before) is a constant - including the sign. It is not enough for the difference between two successive terms (in any order) to remain constant. In the above sequence, the difference is -7 for the first two intervals and then changes to +7. An excellent example of an arithmetic sequence would be: 1, 5, 9, 13, 17, in which the numbers are going up by four, thus having a common difference of four. This fulfills the requirements of an arithmetic sequence - it must have a common difference between all numbers. Common difference, in the context of arithmetic sequences is the difference between one element of the sequence and the element before it. An arithmetic sequence is an ordered set of numbers such that the difference between any two successive members of the set is a constant.

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