![]() ![]() The time interval between the bounces of a ball follows a geometric sequence in the ideal model, and it is a convergent sequence. R 0 if a 1 < 0, the signs related to a n will be inverted. The Sequence diverges – exponential growth, i.e. If common difference is positive (d > 0), the sequence tends to positive infinity and, if common difference is negative (d o In the infinite case (n → ∞), the sequence tends to infinity depending on the common difference (a n → ±∞). The number of terms in a sequence can be either infinite or finite. The set of even numbers and the set of odd numbers are the simplest examples of arithmetic sequences, where each sequence has a common difference (d) of 2. If the initial term is a 1 and the common difference is d, then the n th term of the sequence is given by īy taking the above result further, the n th term can be given also as Ī n = a m + (n-m)d, where a m is a random term in the sequence such that n > m. It is also known as arithmetic progression.Īrithmetic Sequnece ⇒ a 1, a 2, a 3, a 4, …, a n where a 2 = a 1 + d, a 3 = a 2 + d, and so on. More about Arithmetic Sequence (Arithmetric Progression)Īn arithmetic sequence is defined as a sequence of numbers with a constant difference between each consecutive term. ![]() The number of elements in the sequence can either be finite or infinite. The sequence is a set of ordered numbers. Arithmetic sequences and Geometric sequences are two of the basic patterns that occur in numbers, and often found in natural phenomena. Often these patterns can be seen in nature and helps us to explain their behaviour in a scientific point of view. The study of patterns of numbers and their behaviour is an important study in the field of mathematics. Arithmetic Sequence vs Geometric Sequence ![]()
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