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In an arithmetic series, each term is defined by a fixed value added to the previous term. This fixed value (common difference) may be positive or negative.
In a geometric series, each term is defined as a fixed multiple of the previous term. This fixed value (common ratio) may be positive or negative.
The common difference or common ratio can, technically, be zero but they result in pointless series.
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What is the difference between an arithmetic series and a geometric series?
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| < 1 then T(n) tends to 1/(1 - r) as n tends to infinity.
What is a 'series' mean in math?
A series is a sequence of numbers that follows an identifiable pattern. There are two basic forms of series: Arithmetic, where the difference between successive terms is the same number. 1, 4, 7, 10, 13, 16, 19, 21 is an arithmetic series, each successive term is 3 larger than the previous term Geometric, were successive terms are achieved by multiplying each term by the same number 1, 2, 4, 8, 16, 32, 64, 128 is a geometric series, each successive term is the result of multiplying the previous term by 2
How do you find the sum of a series of numbers?
There is no simple answer. There are simple formulae for simple sequences such as arithmetic or geometric progressions; there are less simple solutions arising from Taylor or Maclaurin series. But for the majority of sequences there are no solutions.
What is meant by arithmetic sum?
That refers to the sum of an arithmetic series.
What is the term for A sequence of numbers in which the ratio between two consecutive numbers is a constant?
A geometric series.
