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This icon indicates the slide contains activities created in Flash. These activities are not editable. This icon indicates an accompanying worksheet. 1 of 10 This icon indicates teacherâ€™s notes in the Notes field. To enable the animations and activities in this presentation, Flash Player needs to be installed. This can be downloaded free of charge from http://get.adobe.com/flashplayer/ © Boardworks 2013 Maths for ages 11-16 2 of 10 25 © Boardworks 2013 © Boardworks Ltd 2009 Naming sequences Here are the names of some sequences which you may know already: 2, 4, 6, 8, 10, ... Even numbers (or multiples of 2) 1, 3, 5, 7, 9, ... Odd numbers 3, 6, 9, 12, 15, ... Multiples of 3 5, 10, 15, 20, 25, ... Multiples of 5 1, 4, 9, 16, 25, ... Square numbers 1, 3, 6, 10, 15, ... Triangular numbers 3 of 10 25 © Boardworks 2013 © Boardworks Ltd 2009 Sequences from real life Number sequences are all around us. Some sequences, like the ones we have looked at today follow a simple rule. Some sequences follow more complex rules, for example, the time the sun sets each day. Some sequences are completely random, like the sequence of numbers drawn in the lottery. What other number sequences can be made from real-life situations? 4 of 10 25 © Boardworks 2013 © Boardworks Ltd 2009 Sequences that increase in equal steps We can describe sequences by finding a rule that tells us how the sequence continues. To work out a rule it is often helpful to find the difference between consecutive terms. For example, look at the difference between each term in this sequence: 3, 7, +4 11, +4 15, +4 19, +4 +4 23, +4 27, 31, ... +4 This sequence starts with 3 and increases by 4 each time. Every term in this sequence is one less than a multiple of 4. 5 of 10 25 © Boardworks 2013 © Boardworks Ltd 2009 Sequences that increase by multiplying Some sequences increase or decrease by multiplying or dividing each term by a constant factor. For example, look at this sequence: 2, 4, ×2 8, ×2 16, ×2 32, ×2 64, ×2 128, 256, ... ×2 ×2 This sequence starts with 2 and increases by multiplying the previous term by 2. All of the terms in this sequence are powers of 2. 6 of 10 25 © Boardworks 2013 © Boardworks Ltd 2009 Fibonacci 7 of 10 25 © Boardworks 2013 © Boardworks Ltd 2009 Finding missing terms 8 of 10 25 © Boardworks 2013 © Boardworks Ltd 2009 Name that sequence! 9 of 10 25 © Boardworks 2013 © Boardworks Ltd 2009 Webinar 10 of 10 25 © Boardworks 2013 © Boardworks Ltd 2009