Maths Unit 10 – Sequences Picture sequences Number sequences Sequences can be in the form of patterns or numbers Here is a pattern sequence: To draw the next pattern you need to spot what is happening from one pattern to the other. In this sequence 3 sticks are being added each time. Here is a sequence; In this sequence, 5 is added to the previous term to create the next number in the sequence. The pattern is infinite. Using the nth term You can use the nth term to find a specific number in a sequence. To find the 8th term of a sequence which has a nth term of 6n – 2 you need to do some substitution Step 1 – Replace n with the term number; in this case 8 So, 6 x 8 - 2 Step 2 – complete the calculation So, 6 x 8 – 2 = 46 The 8th term of the sequence is 46 Finding the nth term Here is a sequence. 1, 4, 7, 10. The nth term is 3n-2. To find the nth term you start by finding the common difference between terms. The picture demonstrate the rest of the method to find the nth term. Key words and definitions Term – the position in the sequence Substitution – replacing letters with a given number Sequence – a string of objects which follow a particular pattern. These can be pictures or numbers. Pattern – when a picture or sets of numbers are in a specified sequence nth term – an expression which will allow you to calculate a term that is in a particular position