You'll have found by now that algebra forms a major part of KS3 Maths. In algebra letters are used in place of numbers. The letter n (usually in italics) is often used to indicate the position of a term in a sequence. We call this the 'nth' term.
Finding the rule for a number pattern is usually quite easy but can sometimes be a bit harder. One famous pattern is the Fibonacci sequence. This describes a spiral pattern and is very common in nature. The rule for the Fibonacci sequence is to add the previous two numbers to find the next. The nth term for this would be... advanced mathematics. Don't worry about that just yet!
Here's an easier example. If a sequence begins with 5 and goes up in twos thereafter, the nth term of that sequence would be 2n + 3 (2 x 1 + 3 = 5, 2 x 2 + 3 = 7, 2 x 3 + 3 = 9 etc.). This can be a little difficult to grasp but work through this quiz (and read the helpful comments!) and you will soon get the idea.














In the 1^{st} term the value of n will be 1 and therefore the answer can be found as follows: (3 x 1) + 1

The answer can be found as follows: (3 x 3) + 1


We are told that we need the 8^{th} term. We put an 8 where the n is and then work it out: (3 x 8) + 1

(14 x 2)  6


(4 + 1)^{2}

(2 x 3)^{2} + 1


(5 x n) + 1

These are known as square numbers. The 1^{st} number in the sequence is 1 x 1; the 2^{nd} number is 2 x 2; the 3^{rd} number is 3 x 3 etc.


These are known as cube numbers. The 1^{st} number in the sequence is 1 x 1 x 1; the 2^{nd} number is 2 x 2 x 2; the 3^{rd} number is 3 x 3 x 3 and the 4^{th} number will be 4 x 4 x 4

This is known as the Fibonacci sequence. To find each number you add together the two previous numbers. After 13 comes 21 (8 + 13) and then comes 34 (21 + 13)
