Maths question

[samvimesboots]

Can someone please just confirm that my understanding is correct for problem 15 (answer is attached) .

If an equation has n rather than an x or y should my DC always assume this is a count so all answers should work with n=1, n=2 etc.

Thank you

It’s a sequence rather than a count, n refers to the “number in the list” I.e. n=1 is the first, n=2 is the second etc.

but yes, the correct answer must be valid for all values of n

Thank you that is useful.

Is it safe to assume the sequence will always be 1,2,3 etc unless otherwise explicitly told.

It's conventional to use n or i for sequences, but no guarantee of that.

The fact that it's referring to "this sequence" and then shows a sequence of numbers is what tells you the expression will be evaluated with 1, 2, 3, etc substituted in.

The letter chosen is just convention.

Yes it will always be n=1, n=2 as ‘n’ describes the position in the sequence. Unless you are told, for example, ‘the seventh term in a sequence is…’, then n=7.

It may be worth addressing the misconception in the incorrect answer of ‘n + 7’. The student has an understanding that the sequence increases by 7 each time so has chosen ‘+7’. There is a gap in knowledge there that a sequence that increases by 7 each time is connected to the 7 times table. The 7 times table has the nth term 7n, as it goes 7x1, 7x2 etc. So this sequence must also have a rule containing 7n. As it starts with a number 2 less than 7, it must be 7n - 2.

the gap (7) is the multiplier.
then to find the + or - number find the 0th term (in this case -2) (ie the term that would be the term before the first term)
so the answer is 7n-2

Thanks - I think DC had never come across the concept of n meaning a sequence. DC had solved it by putting 5,12, 19 etc into n so answer A n +5 works
5 +7 =12
12 + 7= 19
19 +7 = 26
I suspect the question was deliberately set up to trip up kids that have not come across n in an equation

Thank you. Looking for the "this sequence" is a great tip

and you are right I need to include in the explanation the connection to the 7 times table. It's a good approach thank you

Exactly. It should hold true for all values of n. The second answer is correct.

Thanks everyone who answered. I know how to explain it now. I really appreciate you all taking the time to help me. Thank you

Sequences are in Foundation level GCSE. There is nothing deliberately set up to trip up students. It is a straightforward question.

This is 11+

Ah OK.
That explains why the answer seems to use trial and error rather than a proper solution!

It is good to know this is foundation GCSE. I might google and see if I can get some more questions DC can practice with. But I think they will get the answer with the explanations people have helped with here

Make sure they are solid that 7n means 7 x n, and that this is transferable to any algebra/letter used. E.g. 3y means 3 x y. This is a really common gap in this age group if it hasn’t been properly taught and explored and can appear in a variety of topics/concepts. Good luck to your DC!

Good tip. I will do.

It's been so long since I've done these topics. I'm quite enjoying revisiting things but I do worry about accidentally teaching DC "the wrong method". Having people who can sanity checking me is great. Thanks

Another example
34, 28, 22, 16, ...

Consistent gap of -6
The 'zeroth' term would be 40.
So the sequence is -6n+40

wonderful. We've been through the question tonight and DC got the concept. I did some simple examples and they got it.

I'll try your example later. Thanks