Nth Term

In this chapter we’re going to explore Nth term. Your will understand the terminology used in sequence questions and then be able to work out the formula for the nth tem of simple arithmetic sequences.
You will learn how to find the nth term of a sequence with any number of terms.

What is a sequence?

A sequence is a set of numbers with a pattern. Each number in a sequence is known as a term.

For example

The sequence; 3, 5, 7, 9, 11
The sequence above has 5 terms whereby to find the next term in the sequence we add on 2 to the previous term. The following table might be useful to observe the connection.

Creating sequences from Nth terms

A sequence has a nth term as 3n+1. Find the first 5 terms.
The above question is asking to find the first 5 terms in a unknown sequence using the pattern; 2n+1.
We know nth = 3n+1
The first nth term becomes;

Second nth term becomes;

…and so on;



The following table shows the numbers in the sequence in a better observation.

So the sequence which has the nth term as 3n+1 is;