hey guys hope you're well welcome to this chapter so we're going to start with constant difference patterns so what is a constant difference pattern well let's say you have the number well the number is 5 8 11 14 and then it goes on and on so we call it a pattern because it's just a whole bunch of numbers but can you see what the pattern actually is well you can see here that we are adding three each time can you see that so because we adding or it could also be subtracting for I'll show you one now if we adding the same amount we call that a constant difference pattern so let's say for example we have um 20 oh that's a different color 20 18 16 14 and so on well now what's happening is we are subtracting two can you see that we are subtracting two each time so we call that that's also a constant difference pattern now the way that this lesson's going to go is we I'm going to teach you how to identify the pattern I'm going to also teach you how to come up with a formula that because that's something that you're going to be asked and then we're going to get more into the details of um you know how to determine specific values and then as we go along we're also going to do two examples where we're looking at tables Okay so we've got quite a bit we're going to cover we're going to go as quickly as we can but obviously I'm going to try and make sure that you understand everything so let's go so here we have a pattern now we can see that we adding two you can see that we adding two each time to go from the next to the next so the first question says determine the rule in words or you could just say um add two that's all that you need to say but now let me show you a nice easy way to come up with a rule using algebra so all I want you to to do now your teacher might use different letters but all I want you to do quickly is just say equals then the number that you are you see this number here that you are adding each time it could also be a negative as we'll see in some examples I want you to write that number down and then put a letter now teachers usually use the letter N okay that's the first thing I want you to do now all I want you to do now is try to work out or calculate what if we had to go backwards if we had to go here what would this number be well we should be able to identify or work out that this number would have to be a one right because if you had to say add two well then it would give you three so you see how we said it's a one that's a positive one so I just want you to put a positive one over there and then your teacher might put something different here but normally or most times teachers will say t n but your teacher might put something different but that's okay you can use whatever your teacher does but what's important is that you know how to find this partt and this pot and this is the rule and we can use that rule to calculate many many things which I'm going to show you in a few examples from now like over here and over here okay so let's practice this a little bit more so here what we can see is we're going from 10 to 14 so we are adding four then we adding four and we adding four you see how it's a constant difference so what is the rule add four easy right now determine the rule okay so remember the number that you are adding or subtracting you put that number there four if it was a negative you would put a negative which we'll see in I think this example okay so we're going to put a four then put a n then you need to imagine what would this number be well this number here would have to be 6 because 6 + 4 is 10 so is it a positive six yes it is you just set positive 6 then you just put a t in or whatever your teacher uses and there is the rule now here's one where you are going- - 2 - 2 so what's the rule subtract two if we wrote it in words now what is the rule using algebra well you take you put a equal sign you take that Min - 2 and you put a n then you have to imagine what would this one be well this would have to be 22 right don't say 18 because it has to be 22 because when you minus 2 then it'll give us 20 so we will say but it's a positive 22 so we'll say positive 22 and then here you can just say TN and there is the rule let's do one more and then we're going to start getting into more detailed kind of things so determine the rule in words so we can add six here then we add six over here because 17 + 6 is 23 and then 2 3 to 29 is also add six so with the rule in words we could say add six now what is the rule in algebra well remember what we said you take that number six and you put a n then you have to imagine what is this number going to be well that would have to be five because 5 + 6 is 11 so we'll say five and then here you can just say TN right now we're going to go and take it a little bit further okay so let's have a look here here we are adding three here we are adding three here we are adding three so it says determine the next two terms well if you add three you would get 32 and if you add three to that you would get 35 now it says determine the rule using words well what are we doing we're adding three so add three determine the rule using algebra okay so here's where we say TN equals now what is the number that we adding each time three so we say 3 n and then you have to imagine what would this number be what would this one be well that would have to be 17 so we say here 17 okay now this is really important and listen carefully now because I have I still have grade 12s that still get this part confused it's not difficult but you just have to think carefully and once you understand it then it's very very easy so you see how we have the number 20 23 26 29 these are called the values those are the values but what is the term well this is term number one term number two term number three and term number four now whenever they give you a value I want you to plug that over here and whenever they give you a term I want you to plug that over here so you have to make a note for yourself of how you are going to remember that so this question number four says what is term which is the blue one 42 so we go to the blue one and we're going to put a 42 there so we're going to go um term so we're just going to go equals 3 now you're going to change this to a 42 in a bracket so now this has become a multiply so it's going to be 3 * 42 + 17 and that will give you 143 okay so we're going to put 143 over there now with this one they said which term has a value of 245 so they're giving us the value now okay um they're giving us the value so we take our little formula that we have and we rewrite it um you know the way we had it you don't you don't write the 42 for example we don't know what this is now because now it's a brand new question so the value which is the yellow part is going to be 245 so we put 245 in the place of that there we go now when you look at this what are we actually trying to find we trying to find this one maybe you can remember from a previous grade where we did equations and you had to solve for x well now we're just solving for n okay so the way it works is we want to keep so let's just keep these two together for now and we want to keep all of the things with letters which is this it's got the letter N we want to keep that on one side and everything else we want to take it to the other side so let's keep this 3 n here on the on this side let's keep it over there and then that means we need to take this 17 and we need to take it to the other side so we're going to take this 17 over to here the rule is you see how it's a plus when it crosses this sign over here the equal sign then this symbol has to switch to a negative if it was a negative then it would switch to a positive so we're going to say 2 4 5 and now we're going to say minus 17 you see how we took it to the other side and then we changed it to a minus and then we have that and so if you minus those two numbers you end up with 22 28 like that okay I'm just going to write it up here because I'm running out of space now the next thing we need to do is we need to get rid of this three the way you do that is you divide by three here so that those cancel but what you do on the one side you have to do on the other side so now we have n and on the other side if you divide those you get 76 so that is the answer which term term number 76 okay it might still be feeling a bit weird but luckily we still have another two more of those to practice so here let's try this one now so here we can see that we are adding five adding five adding five adding five adding five so it says write down the next two terms well if you add five to 31 you would end up with 36 and if you add 5 to 36 you would end up with 41 now it says use a Ru find a rule using words well here you can just say add five technically if they say words we could say add five like that um and then this one says determine the rule using algebra okay so remember here's where you say equals then the number that you are adding or subtracting each time you put that number here okay if it was a negative you would put a negative and then you need to remember you need to figure out what is this number going to be over here so this would have to be a six because 6 plus 5 would give you 11 so this would be six and then here you can just put T in but like I I said your teacher might use a different letter or a different thing over there now this formula is now going to be very important when we go to question four and question five so remember what I said when you've got the 11 um 16 21 26 and then you've got um those are called the values and then you've got term which is one that's term two term three it's almost like position position one position two position three position four so if I write down the formula remember that this one here which is the term that goes here a lot of Learners get confused because they see that there's a T and A T but it's not they don't go together and then this is the value so if they give you the value then you plug that in here so this first question says determine term 20 okay so they've given us the blue one so we go and we fill in the blue one like that and so that becomes a multiply so you can can rewrite it as 5 multi um 20 + 6 and if you had to work that out you'd end up with 106 now with number five now they're saying which term has a value so now that's the yellow one okay so we're going to write down the formula and you're going to put the value the yellow one which goes in that place as 261 now remember we want to get this part by itself so we take this Plus six over to the other side so it becomes a minus when you take it to the other side and then what is 261 - 6 it's 255 okay let's just write that over here now remember at this step you divide by five and what you do to the one side you do to the other side so that those fives cancel and so you end up with 51 so the answer here is 51 and I should have also put here 106 let's do another one determine the next two terms okay so if you look at 11 and 8 you can see that we are actually minusing three so what is 2 - 3 well that will actually give you -1 and then what is -1 take away three well that'll give you -4 now it says determine the rule well the rule is subtract three now it says find the rule using algebra okay so remember you say TN equals now what are we doing here we minusing three so you put a minus 3 and then you put the N then remember you need to try figure out what is this number over here if we had to have a number here what would it be well it would be 14 why because 14 - 3 would be 11 so it's 14 like that now remember that the 11 the eight eight the five the two those are the values and then the term is well that would be term number one term number two term number three term number four and then when we write out the formula minus 3 n + 14 then remember that the term is this one and the value is this one so with number four they say determine term 20 which is the blue one term 20 so we're going to take that formula and we're going to plug in a 20 over there and that's the same as multiplying and so you could just go type this all on your calculator and you'd end up with - 46 so the answer there is 46 now with number five we write down our formula again now they say which term has a value okay so the value is the yellow one so it goes there so we put -28 over there now we need to get this part by itself so we take this to the other side we take that over to the other side so it will become -4 and if you had to type this on your calculator this will give you 42 so let me just write that over here now to get now listen carefully to get this by itself you're going to have to divide by3 so you divide by -3 and what you do on the one side you do on the other side so that those can all cancel and then you're left with 14 so we can put 14 as our answer over there with these types of table questions they very easy have a look here term one term two term three is 5 8 and 11 so that's almost like me telling you 5 8 11 you see very very easy now it's exactly the same as what we looked at in the previous one they're just showing it in a different way so all that they want you to do here is to determine the letter a and the letter B so what they actually want is what is term number six well that's easy if we just had to carry on here can you see that we adding three each time so that would be 17 and then that would be 20 so term 1 2 3 4 5 6 will be 20 and then term 7 will just be 23 let's do one more here we have term one 2 and three so we can see that it's 19 16 and 13 so what are we doing here we subtracting three so if we just keep subtracting 3 this will be 7 4 1 so term number 1 2 3 4 5 6 will have a value of four and then term number seven by the way this just means that we skipping so we we we don't want to look at term four and five we're just skipping and then this term seven would be four 5 6 7even it would be this one over here which is a one so the answer is four and one