![]() For instance, the series 8, 4, -2, 1, -1/2 … is a Geometric Progression (GP) for which -1/2 is the common ratio. The nth term will beĪ geometric progression is a series in which each term is obtained by a multiplication or division of the next term, by a fixed or common number. The established form of AP is a, a + d, a + 2d, a + 3d and ….so on. The progression -3, 0, 3, 6, 9 is an example of Arithmetic Progression (AP) that has three as the common difference d. For instance, the series, 9, 6, 3, 0,-3 and so on, is an arithmetic progression with -3 as the standard difference. Ref Fig.3 below.Īn arithmetic progression is a series or sequence of numbers in which each term is derived from the next term, by adding or subtracting a fixed or common number called the common difference d. It is due to the fact that if you divide or find the ratio of the successive terms, you get a common or standard ratio. It is essential to note that the common number that multiplies or divides at each step of a geometric sequence is called the ratio r. Let us take another example, 81, 27, 9, 3, 1 …it is a geometric sequence as each step divides (or multiplies) by the number 3. The reason being that each step multiplies by two. For example, 2, 4, 8, 16, 32 … is a geometric series. In simple words, a geometric sequence moves from one term to the next by always multiplying (or by division) by the same common value or number. We obtain results by multiplying the terms of a geometric sequence. Ref fig 2 belowĪ geometric sequence or geometric series is a geometric order. The reason is that if you add or subtract (also known as finding the difference), you always get the same common value. It is essential to note that the number that is added or subtracted at each level of an arithmetic sequence is called as the difference (d). 7, 3, -1, -5 …is an arithmetic sequence as each step subtracts 4. The same holds for a reverse order (in subtraction). 2, 5, 8, 11, 14….is arithmetic sequence as each step adds 3. Let us take some examples to understand better. Here, in this sequence, each number moves to the second number by adding (or subtracting 1). In the arithmetic sequence, one term goes to the next term by always adding-for example, 1, 2, 3, 4, 5 ….10, and so on. Let us understand the Arithmetic sequence formula. A geometric sequence is about multiplying (or division) in a set order. An arithmetic sequence is about addition (or subtraction) in a set order. ![]() In the geometric series, the common value is always 2. ![]() Ref the figure below, in the arithmetic sequence the difference (d) is always a standard value 7. The geometric progression goes from one term to another and multiplies or divides. An arithmetic sequence is about numbers that add or subtract. Now, the point is what is a sequence and how is it related to the subject of Mathematics. ![]()
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