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# Number Sequences

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### Number Sequences

1. 1. Number sequences<br />BTEOTSSSBAT write down the next term in a sequence and describe sequences using the nth term<br />
2. 2. Key terms<br />Term<br />Sequence<br />Difference method<br />Formula<br />nth term<br />
3. 3. A number sequence is a set of numbers with a rule to find every number (term) in the sequence.<br />For example: we can describe a sequence by n + 1. <br />INPUT<br />OUTPUT<br />n + 1<br />
4. 4. The letter ncan represent any number – in For example 1, 2, 3 and 4. <br />These are then the first four terms of the n = 1 sequence.<br />INPUT<br />OUTPUT<br />1<br />n + 1<br />2<br />
5. 5. The letter ncan represent any number – in For example 1, 2, 3 and 4. <br />These are then the first four terms of the n = 1 sequence.<br />INPUT<br />OUTPUT<br />2<br />n + 1<br />3<br />
6. 6. The letter ncan represent any number – in For example 1, 2, 3 and 4. <br />These are then the first four terms of the n = 1 sequence.<br />INPUT<br />OUTPUT<br />3<br />n + 1<br />4<br />
7. 7. The letter ncan represent any number – in For example 1, 2, 3 and 4. <br />These are then the first four terms of the n+ 1 sequence.<br />INPUT<br />OUTPUT<br />4<br />n + 1<br />5<br />
8. 8. We can put these results in a table:<br />The sequence 2,3,4,5 can be called the n + 1 sequence<br />
9. 9. Write down the sequence of 2n<br />INPUT<br />OUPUT<br />1<br />2<br />3<br />4<br />2n<br />
10. 10. Write down the sequence of 2n<br />INPUT<br />OUPUT<br />1<br />2<br />3<br />4<br />2<br />4<br />6<br />8<br />2n<br />
11. 11. The difference method<br />One method to find the next terms and also to find a formula to describe the sequence is the difference method.<br />1 3 5 7<br />9<br />2<br />2<br />2<br />2<br />The difference between each number is 2, <br />so the next number will be 7 + 2 = 9; <br />the next one after that will be 9 + 2. <br />The rule for this sequence is add 2.<br />
12. 12. Now try these 1<br />Find the next two numbers in the sequence and a describe the rule for the sequence<br />(a) 5, 10, 15, 20, ...<br />(b) 6, 5, 4, 3, 2.....<br />(b) 4, 8, 12, 16, ...<br />(c) 1, 3, 6, 10, .....<br />(d) 5, 10, 20, 40, .....<br />(e) 50, 40, 30, 20 .....<br />
13. 13. Finding the nth term<br />The difference method can be used to find a rule to find any term. <br />Example<br />Find the nth term for the sequence 4, 8, 12, 16, ...<br />
14. 14. Example<br />Find the nth term for the sequence 4, 8, 12, 16, ...<br />Solution<br />The difference is 4– this tells us that the nth term with involve 4n<br />We now need to see what the sequence 4n looks like and compare it with the original sequence<br />There is no difference between 4n and the original sequence. <br />So our sequence is 4n. The nth term is 4n.<br />
15. 15. Example<br />Find the nth term for this sequence: 5, 8, 11, 14 and hence find the 20th term.<br />The difference is 3; this tells us that the nth term will involve 3n.<br />3n is 2 short of the original sequence. So, the nth term will be 3n + 2.<br />The 20th term means that n = 20:<br />3 20 + 2 = 62.<br />The 20th term is 62.<br />
16. 16. Now try these 2<br />Find the nth term for each of the following number sequences:<br />(a) 1, 5, 9, 13, ...<br />(b) 7, 9, 11, 13 ...<br />(c) 4, 5, 6, 7, ...<br />(d) 11. 21, 31, 41, ...<br />(e) 6, 11, 16, 21, ...<br />