However, since these will not be cropping up on the exam then we will not go into too much detail, but if you wish to research the uses of these types of sequences please feel free. These types of lists are formed from using the number of the value to a certain indices, so they will use, etc.

For your exam you will not be required to calculate rules for a list which involves jumps of different sizes, e.g. Form an equation using the multiplier of and the difference added on.Īt times we may come across a sequence which is slightly more complicated than the ones we have just looked at.Now we find the values of the multiplier multiplied by and find the difference between these values and the actual value in the list.This will be the multiplier of in our equation for the sequence. First, we need to find the difference between each individual jump in the list of numbers given.Therefore, we can simply add this to our equation and we have an equation that gives the correct answer every time! We end up with Method If we work out the answer that would give us as below then we can find the difference between the values found using this and the actual values that we have from the list given: Number in list ( n)įrom this table we can see that the difference between the actual values and the values for is always. However, if this was the equation we would find for say the 3rd result an answer of which is incorrect as the real answer is 13. Since every increase of 1 in the n column results in an increase of 5 in the result we must use the value in our equation to ensure that the jump is correct. To determine an equation using the number in the list ( n) we must try to find a rule that works for all of the numbers in the above table and for ones that are not incorporated here also. Therefore, we can say that each step up the list results in an increase of 5 in the number. Exampleįind a pattern in the numbers 3, 8, 13, 18, 23, 28…Ĭlearly, the list starts at the number 3 and then each number after increases by 5. This will obviously save us a lot of time and effort as we will not need to find irrelevant answers and only the one which we need. Then we can make a rule to find any number in the list, say the 34th, without having to work out the other 33 numbers that will appear before this value.

So the first number will be the 1st and then the 2nd and so on. To do this we need to realise that we can label the different values in a list by the times at which they appear. Using the nth termĪ very useful technique which we can make use of with sequences is to use the th term to display a sequence which can then be used to find any number in the sequence. Different patterns can use different rules such as addition, multiplication, indices etc. For example, in this sequence we are adding 4 every time and start at the number 1. With the use of certain rules we can even find the correct value for any number that will occur in the sequence.Ī list of numbers such as 1, 5, 9, 13, 17… can be examined and a pattern found. This can then help us to determine the next number in a sequence by extending the pattern that we have found. A sequence is just a list of numbers that follows a specific pattern.

Different types of sequences gcse maths