Lesson video

Hi everyone, and welcome to today's lesson.

We are going to be looking at descending sequences today.

So I want you to have a little thing before we begin about what descending actually means and what it's going to mean to have a descending sequence.

So before we can begin again, make sure you've got pen and paper, it's really important that you're writing things down as we go and make sure you've got at least any distractions are away, turned off and you've got a nice quiet space to work if possible.

Pause the video now to make sure you've got all of that before we can begin.

Okay, let's make a start.

So the first thing I would like you to do is to describe the sequences in the highlighted columns, so these columns here.

What I would like you to do is think about what is the same about those columns and the sequences in them and what is different.

So pause the video to have a go at that.

Now there are lots of things that you could have said here.

So just because you didn't get these three specifically doesn't mean you're wrong, but these are just some examples.

So I noticed that each sequence has a difference of five in some way.

However, one is increasing by five, this one is increasing by five and the other two are decreasing by five.

Think about how that's probably linked to what we're looking at today.

Two start with four and one starts with negative five.

Well done if you've got any of those and well done if you've got any extras as well, that's brilliant.

You can use tracking calculations and nth term rules remember nth term you also could position to term, so remember they are the same thing.

To describe descending arithmetic sequences.

So I asked you to have a think about what descending means.

What did you think it meant? Hopefully you recalled that actually means going down or decreasing.

So these sequences are decreasing.

So for example, you've got the sequence negative five, negative 10, negative 15, negative 20, negative 25, which is decreasing by five each time.

That means each row if it's decreasing by negative five each time we'd do negative five multiplied by that row number.

So if we had a row n, that would be negative five multiplied by n, which would mean the nth term is negative 5n.

And another example, we've got the sequence four, negative one, negative six, negative 11, negative 16.

Again, we are decreasing by five, so I know it's going to have negative 5n in it.

However, to get from my negative fives, my sequence negative five, and I've got to increase it or shift it up by nine.

So my nth term will be negative 5n add nine.

Pause the video here to complete your independent task.

Your independent task was a matching exercise.

So you had some sequences, we had some nth term rules and we had some descriptions of the sequence.

And you had to match them up and fill in any gaps.

Hopefully you managed to get some of these or all of these answers.

When we had a sequence like one, negative three, negative seven, negative 11.

I knew I was going down by four, decreasing by four.

So I'd going to have negative 4n.

And that negative 4n has been shifted up by five.

So my nth term is negative 4n add five.

This could be described as a sequence starts at one and decreases by four.

These are all you might notice very similar sequences, and that was done to just try and get you really thinking about what the 4n or negative 4n means and what the five or negative five actually means.

So well done if you've got those correct.

Now we got the explore task, so we've got Xavier and Yasmin are discussing the arithmetic sequence below.

Two, five, eight, 11, 14.

Xavier says, "I'm going to multiply every term in the sequence by three." Yasmin says, "I'm going to multiply every time in the sequence by negative one." What I would like you to do is to tell me how the sequence will change.

So maybe you are going to try and multiply every one of those terms, by what you think these two people have said.

I then like you to tell me how the nth term rules have changed.

So you going to need to find the nth term to rule of this one, and then find the nth term all of your new sequences.

Pause the video to do this.

So well done if you found the nth term of the sequence, it was increasing by three.

So my sequence is 3n shifted down by one.

How will the sequences change? Xavier's sequence now becomes six, 15, 24, 33, 42 because it's been multiplied by three.

Yasmin's has become negative two, negative five, negative eight, negative 11 and negative 14.

So Yasmin's sequence has changed by becoming a descending sequence, descending arithmetic sequence.

The nth term rules have changed.

So if we look at Xavier's nth term rule they are increasing by nine, so 9n and shifted down by three, 9n subtract three.

Yasmin's is decreasing by three.

So it's negative 3n and to get from negative 3n we've got to shift up by one to get Yasmin sequence and negative 3n add one is her nth term rule.

And you may have even spotted an extra well done if you have.

That to get from this nth term in the original sequence to say Xavier's.

Both the difference between each sequence, the coefficient n, has been multiplied by three.

And how far it's shifted has been multiplied by three.

Same with Yasmin's, both the difference has been multiplied by negative one and how much it's been shifted either way has been multiplied by negative one.

So excellent job if you manage to make that link and that connection.

So once again, share your work with your class teacher.

I'm sure they'd love to see it or share your work with Oak National or both.

If you'd like to please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

It would be great to see some of your fantastic work.

And I'll see you again next time.