Sequences is a list of numbers which follow a certain rule set. In sequences, each number is called a term and terms next to each other are called consecutive terms. When solving sequences, it is also important to know the position of the terms to help with the definition of the sequence.
2, 5, 8, 11, 14, 17, 20……..
2 – is the first term
17 – is the sixth term
Sequences from term-to-term rules
To define a term-to term sequence, the first term is needed to know what is done to give the next term.
-7, -4, -1, 2, 5
The first term is -7 and the term-to-term rule is “plus 3.”
Sequences from position-to-term rules
To define a position-to-term rule a formula is used to determine the nth term of the sequence.
In this scenario, it is suggested that the terms are inserted into a table.
In this example the nth term of the sequence is n²
Writing sequences from position-to-term rules
The nth term is also called the general term which is also represented as . Therefore the following is true:
1st term is called U1, 2nd term is called U2 etc.
If the nth term of a sequence is 5n – 6 then the rule is written as:
= 5n – 6