Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
Welcome to our Math lesson on Understanding Sequence Notation, this is the third lesson of our suite of math lessons covering the topic of Working with Term-to-Term Rules in Sequences, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
So far, we have shown some of the first terms of a sequence to help you in identifying the pattern. However, this method (known as the list method of representing sequences) is not very helpful when we want to find terms of a given sequence that are far from the first terms. Therefore, we often use algebra to show a sequence and its pattern, as this helps generalize the approach. In this case, we say to have used the sequence notation to provide information about a given sequence.
Thus, we denote any term of a sequence by a letter (usually x, y, u or a) and a number as an index (usually starting from 1 but sometimes the index starts from 0; however, here we will start from 1) to show the number of term in a sequence. We express the general term of a sequence by the index n. Hence, xn indicates the general term (the nth term) of a sequence, x1 indicates the first term of a sequence, x27 the 27th term of that sequence, and so on.
The pattern of a sequence is given by using the sequence notation too. For example, the mathematical sentence
indicates that any term of the given sequence is obtained by multiplying the previous term by 3 and subtracting 2 from the result. Thus, if x1 = 6 and the 8th term of the sequence described above is required, we write
As you see, the sequence notation allows us to find as many terms as we want in a sequence, even if the terms are big numbers. In addition, you don't have to care about identifying the pattern, as it is already given. Another advantage of the sequence notation is that one can easily process the info provided in this form using computer systems.
The first term of a number sequence is -3 and its general term is xn = 11 - 2xn - 1. Find the fifth term of this sequence.
Using the procedure described above in theory, we obtain
As you see, the sequence notation helps in dealing with sets of numbers that at a first glance do not have anything in common with number sequences. In other words, if we didn't have the general term of the above sequence given, it would be very difficult to spot any pattern in the set of values {-3, 17, -23, 57, -103, …}.
Enjoy the "Understanding Sequence Notation" math lesson? People who liked the "Working with Term-to-Term Rules in Sequences lesson found the following resources useful:
Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
We hope you found this Math tutorial "Working with Term-to-Term Rules in Sequences" useful. If you did it would be great if you could spare the time to rate this math tutorial (simply click on the number of stars that match your assessment of this math learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of math and other disciplines.