Lesson video

Hi everyone and welcome to our final lesson in the sequences topic and today's lesson is all about finding the term-to-term rule.

So, before we can begin, make sure you've got a pen, paper.

Make sure you've got rid of any distractions and that you are ready to learn and you've got a nice quiet space if you can find one.

Pause the video here to make sure you've got all of that.

So, now we can begin.

What is the same or different about the sequences below? So you're looking at the numbers in them maybe the difference, maybe you can even find the nth term or perhaps you're looking at the first term, what what is the same or different? Once you've thought about that, I would like you tell me what could the next term be in each sequence.

Pause the video here to do that.

Oh, we could have had lots of things from the same or different.

An example would be all have one as their first term.

Another example purple and orange are being multiplied by a constant to get to the next term.

So the purple one is being multiplied by negative two and the orange one is being multiplied by a half.

Pink has been added to get to the next term so each one has a constant difference so it's been added by three.

So that means we can find the next term in all of those sequences because this one which is multiplied by negative two to get sixty-four.

This one we've just multiplied it by half.

This one we've just added three and this one, hopefully you might've noticed the difference is going up by one each time so this is adding two, adding three adding four, five, six, and then adding seven to get to twenty-eight.

Really well done if you got those especially that green one, that one was slightly trickier, we've not really seen anything like that before so really well done.

How could you describe the pattern in these sequences? So this is very much linked to what we've just done and we've seen what it is that's happening to each term and that's how we found that next one.

Term-to-term rules can describe how we move from one term of a sequence to the next.

So as an example, for this one, the term-to-term rule is just add three, we talked about it earlier we're adding three each time to get from one term to the next, and so that's the term-to-term rule.

What I would like to know is what's the term-to-term rules for the other sequences so pause the video now to have a look at that.

Here are the term-to-term rules.

This one is multiplied by negative two each time.

This one is multiplied by half each time and this one we are adding one extra that we added from the previous term.

And that's, that's as simple as that and that's what the term-to-term rule is and actually the term-to-term rule often very much easy, it's fun and the nth term or the position to term rule.

Now have a go at your independent task so pause the video here to complete that.

You were given the starting point and the term-to-term rule so that you could write out the first five terms of the sequences.

So if this one starts at two, the term-to-term rule is triple the current term so each time I'm multiplying it by three and I'll put the rest of the answers up in a minute.

For the second question you were asked to find the term-to-term rules.

So you might be adding, subtracting, multiplying, dividing, there might be something different.

So for this one, for example, each time you're multiplying by two, so that would be the term-to-term rule.

And here are the rest of the answers.

Really well done if you managed to get B I thought that one was particularly a little bit tricky, because we were squaring the current term, so three squared is nine.

Nine squared is eighty-one, so each time that's what you were doing.

Now for your explore task.

Cala and Xavier have come up with term-to-term rules.

They want to try their rules on different starting numbers as the first term.

So Cala is saying to generate a new term I square the current term, so that's her term-to-term rule.

Xavier is saying to generate a new term, I double the current term and then add five.

And here are all the possible starting numbers so you've got five different starting numbers.

I would like you to find the sequences using their term-to-term rules and each of those starting numbers so you're going to get a lot of practise in doing this.

Once you've done that, I would like you to have a think about what is the same or different about the sequences they form so you're going to give me some things that are the same and some things that are different about those sequences that they have created.

Pause the video now to have a go at that.

So here are all the different sequences that we could have created using the starting numbers and Cala and Xavier's term-to-term rules.

What's interesting is that if we're squaring zero, we just continue to get zero and that's still the sequence even though it's the same number repeating itself.

We've got lots of other great sequences as well, squaring the term you can see actually this is one of the things that I noticed and one of the differences I noticed that Cala does not have any negative terms with the exception of the first one, because remember if you're squaring a negative, you're going to end up with a positive.

For Xavier, he's also got some nice sequences here but he has got negatives other than the first term because he's just doubling and adding five, so there's no reason that he couldn't generate some negatives in his sequences.

Both of these two people have ascending and descending sequences.

Have a think about what ascending and descending means.

Ascending means increasing.

Descending means decreasing, good.

So both of them have both of those different types of sequences.

Can you see which one the descending sequence is in Cala's? Hopefully you can spot that it's actually this one because those fractions are getting smaller.

Imagine half a pizza, imagine quarter of a pizza, quarter is smaller so that's actually descending.

In Xavier's sequences, the difference between each term doubles each time so I actually found the difference between each of the terms in the sequences and that difference is doubling each time so well done if you spotted that.

Well done as well if you managed to find the nth term of some of them and noticed something interesting about that, there were lots of things you could've thought about that were similarities and differences, so please do share them with your class teacher or with somebody at home.

That brings us to the end of our lesson and the end of entire topic on sequences.

So remember to do the quiz at the end of the lesson to just check your understanding and make sure don't have any misconceptions because this topic is now done so you just need to check that you understand all of that.

So thank you very much for being a part of this sequences topic.

I've really enjoyed working with you and I hope you enjoyed these lessons, too.