This is a type of number sequence where the next term is found by adding a constant value to its predecessor. There are many number sequences, but the arithmetic sequence and geometric sequence are the most commonly used ones. The pattern of the sequence is, therefore, the addition of 8 to the preceding term. Identify the pattern of the sequence by finding the difference between two consecutive terms. What is the value of n in the following number sequence? The missing terms are therefore: 8 + 4 = 12 and 16 + 4 = 20 You can notice that the corresponding number is obtained by adding 4 to the preceding number. Three consecutive numbers, 24, 28, and 32, are examined to find this sequence pattern, and the rule obtained. The consecutive number is obtained by adding 3 to the preceding integer.įind the missing terms in the following sequence: The other list is a sequence because there is a proper order of obtaining the preceding number. The first list of numbers does not make a sequence because the numbers lack proper order or pattern. For this case, it is important to learn and practice number sequence.
By learning and excising number sequence, an individual can sharpen their numerical reasoning capability, which helps our daily activities such as calculating taxes, loans, or doing business. Logic numerical problems generally consist of one or two missing numbers and 4 or more visible terms.įor this case, a test designer produces a sequence in which the only one fits the number. A sequence that continues indefinitely without terminating is an infinite sequence, whereas a sequence with an end is known as a finite sequence. They have important applications in physics, engineering, biology, economics, computer science, queueing theory, and finance.Number sequence is a progression or an ordered list of numbers governed by a pattern or rule.
Geometric sequences are used throughout mathematics. The geometric sequences have played an important role in the early development of calculus, and continue to play a central part in the study of the convergence of series. The following are the general applications of geometric sequence in real life – Applications of Geometric Sequence in Real Life Hence, the sum of 7 terms of the geometric sequence, 3, 6, 12, ……. In other words, a sequence, a 1, a 2, a 3, ……… a n is called a geometric progression if $\frac$] = 3 ( 128 – 1 ) = 381 The constant ratio is called the common ratio of the geometric sequence. P ) if the ratio of a term and the term preceding it is always a constant quantity. What is a Geometric Sequence?Ī sequence of non-zero numbers is called a geometric sequence, also known as geometric progression (G. Let us now understand what we mean by a geometric sequence. The terms of this sequence 1, 1, 2, 3, 5, 8, ……. For example, the Fibonacci sequence is given byĪ 1 = 1, a 2 = 1 and a n + 1 = a n + a n – 1, n ≥ 2 Sometime we represent a real sequence by using a recursive relation. is a sequence whose nth term is ( 2n – 1 ).Īnother way of representing a real sequence is to give a rule of writing the nth term of a sequence. One way to represent a real sequence is to list its first few terms till the rule for writing down other terms becomes clear, for example, 1, 3, 5 …. There are several ways of representing a real sequence. In other words, a real sequence is a function with domain N and the range a subset of the set R of real numbers. What is a Real Sequence?Ī sequence whose range is a subset of R is called a real sequence. If a n is the nth term of a sequence, ‘a’ then we write a =. a 1, a 2, a 3, ……… a n are known as first term, second term…… nth term respectively of the sequence. under a sequence ‘a’ are denoted by a 1, a 2, a 3, ……… a n respectively. since the domain for every sequence is the set N of natural numbers, therefore, a sequence is represented by its range. It is compulsory to denote a sequence by a letter ‘a’ and the image a(n) of n ∈ under a by a n. In order to study geometric sequence, it is important for us to understand what we mean by a sequence?Ī sequence is a function whose domain is the set N of natural numbers. Applications of Geometric Sequence in Real Life. Finding the Sum of a Given Number of Terms of a Given geometric Sequence. Finding the Position of a Given Term in a Given Geometric Sequence. Finding the indicated Term of a Geometric Sequence when its first term and the common ratio are given. 
5 examples of geometric sequence with solution series#
Examining Geometric Series under Different Conditions.
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