![]() If you need someone to explain this method to you in person, book in a free taster session here.įor even more linear nth term questions, try our nth term worksheet. Have a go at finding the nth term of each of these sequences and put your answers in the comments or email them to and I’ll let you know if you got them right. If you are studying the higher tier, you can read my guide on how to find the nth term of a quadratic sequence.īelow are 10 linear sequences. So there is an introduction to the nth term and how to find the nth term of a linear sequence. N = 1 -3×1 + 14 = 11 this matches our sequence Let’s check the first three terms just to be sure… If the number you get is not an integer, then this means the number is not in the sequence. ![]() If the number you get is an integer, then this means the number is in the sequence. It makes sense to say that 665 is the 100 th term in a sequence, but not that it is the 100.6 th term in the sequence. However, if we don’t get a whole number, this makes no sense. And then solve it! This will basically do the opposite of what we did in the previous example – it will tell us what number in the sequence 665 is… if the number we get is a whole number, that will make sense. Let’s say I was asked “Is 665 in the sequence?”.Īgain, without the nth term, the only way to do this would be by writing out the sequence until we get to 665 and see whether it appears… but that’s going to take even longer than the last question!Īgain, the nth term can make this a lot easier and quicker for us.Īll we need to do is take our nth term formula, and make it equal to the number we are testing (in this case it’s 665). Let’s say we are still looking at the same sequence – 5, 9, 13, 17, … Much quicker than writing out 200 terms I’m sure you would agree! So in a matter of seconds we know that the 200 th term in the sequence is 801. With the nth term, you can get it instantly. ![]() If you had never heard of the nth term before, the only way you would know how to do this is to continue writing out the sequence until you get to the 200 th term… which would be time-consuming to say the least! So it is fairly easy to find the next few terms in the sequence.īut where the nth term becomes really useful is if I asked you to find the 200 th term in the sequence. You can clearly see here that the sequence we have generated is linear and goes up by 4 each time. So we know the sequence starts 5, 9, 13, 17. I can find the 2 nd, 3 rd and 4 th terms as well too. Therefore I know the first term in the sequence is 5. If I wanted to find the 1 st term in the sequence, I can do that using the nth term. So let’s say a sequence has nth term 4n + 1. The nth term is a formula in terms of n that will find any term in the sequence that you want. What is the nth term, and why is it useful?įirst of all, let me explain what the nth term of a sequence is. This is a relatively simple process, but is incredibly useful. I have a few up my sleeve that I am currently trying out, and I am always open to contributions from others! 1.Following on from the last blog on identifying different types of sequences, in this blog I will show you how to find the nth term of a linear sequence. In the whole class discussion that follows, I am then able to direct their attention to relationships that exists between the rows.Īnyway, I hope you and your students find these Fill in the gaps activities useful. Most focus their attention across the page, moving forwards and backwards across each row. ![]() Watching students work through these is fascinating. But it is easier to use this Rule: x n n (n+1)/2. This allows flexibility for students to describe the order they solved each problem during the whole class discussion. The Triangular Number Sequence is generated from a pattern of dots which form a triangle: By adding another row of dots and counting all the dots we can find the next number of the sequence. I have animated the PowerPoint so you can click on the boxes in any order to reveal each answer. I may start these types of activities with an Example-Problem Pair or, depending on the class and the situation, I may just give out the activity cold. I use them as a way of bringing together several concepts, challenging students to work forwards and backwards across rows, to ensure they do not get tied into one way of thinking. Whilst it still fits under my definition of Intelligent Practice (and as such, the guidance notes for running these types of activities should still be useful), I see these more of a revision activity. It is my attempt to replicate some of my favourite Standards Units card sort activities, but with less cutting and some elements of variation. This is a new type of activity I am working on, with the catchy name of Fill in the gaps.
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