Infinite SequenceĪn infinite sequence is similar to a finite sequence in that we can have as many terms as we would like. No matter how large that nth term is - whether it’s the 100th term or the 1,000,000th term, the sequence is still considered finite if it has a value that we know. When we write the notation for any sequence, we usually talk about an ‘ nth’ term.Ī finite sequence is a sequence that has an nth term. Strictly DecreasingĮach successive number is only less than the previous oneĮach successive number can be less than or equal to the previous oneĪ finite sequence is defined as a sequence that has an end. Check out the table below for the definition. This is defined as a strictly decreasing monotonic sequence. Each successive number is less than the one before it. In this example, you can see that there are 4 numbers, represented by the subscript in. In a decreasing monotonic sequence, each number after the first number, represented by, is less than the one before it. Strictly IncreasingĮach successive number is only greater than the previous oneĮach successive number can be greater or equal to the previous oneĪ decreasing monotonic sequence is a similar concept to an increasing monotonic sequence. This is defined as a strictly increasing monotonic sequence. Each successive number is greater than the one before it. In an increasing monotonic sequence, each number after the first number, represented by, is bigger than the one before it. A monotone sequence has only one pattern. The most common way is to see whether a sequence is a monotone sequence or not. There are a couple of different ways we can define a sequence. While there is no single way to check whether something is a sequence or not, you can usually tell by subtracting or dividing each successive number by the previous number. Random patternĪ pattern that is not strictly defined by the below This pattern can be any of the following described in the table below. A sequence is defined as a list of numbers that follow a pattern. Successive is another way of saying one after anotherġ, 2, 3, 4 - in this example, 2 comes immediately after 1 3 after 2, etc. Numeric PatternĪ numeric pattern is a trend that you can see in a group of numbers Is 22 a number in the sequence with nth term = 4n+1 ?Īs 5.25 is not an integer this means that 22 is not a number in the sequence.In order to understand what a sequence is, you should first understand two very important concepts. If n (the term number) is an integer the number is in the sequence, if n is not an integer the number is not in the sequence. In order to work out whether a number appears in a sequence using the nth term we put the number equal to the nth term and solve it. In order to find any term in a sequence using the nth term we substitute a value for the term number into it. Mixing up working out a term in a sequence with whether a number appears in a sequence.Quadratic sequences have a common second difference d 2.Geometric sequences are generated by multiplying or dividing by the same amount each time – they have a common ratio r.Arithmetic sequences are generated by adding or subtracting the same amount each time – they have a common difference d.Mixing up arithmetic and geometric and quadratic sequences.
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