# Tough nth term Question Watch

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This is a question from an additional maths paper which I have been dwelling on for the past 2 hours or so. I have the mark scheme and hence the answer but I do not understand how it is solved. Please explain if you can make out how. For e.g., why isn't (a)(ii)3.5n or 4n - 1 ?

I understand (a)(i) and (b)(i) since they are really obvious but the rest literally makes me want to strangle a new-born baby.

The question:

(a) An artist makes a sequence of patterns.He uses three types of metal pieces called rods, springs and bobs.He welds them together to make patterns.

In Pattern 2 there are 7 rods, 8 springs and 2 bobs.

In Pattern n there are n bobs.

(i) How many springs are there in Pattern n?

(ii) How many rods are there in Pattern n?

(b) The artist now changes his design to make new patterns with greater widths.The pattern below is called Pattern 3 by 2.In Pattern x by y there are xy bobs.

(i) How many springs are there in Pattern x by y?

(ii) How many rods are there in Pattern x by y?

The answer in accordance to the mark scheme:

(a) (i) 4n

(ii) 3n + 1

(b) (i) 4xy

(ii) Strategy,

e.g. simplify then extend or lookat vertical and horizontal Method leading to correct answer,

e.g. notices 1more row to dimension comparison (x+1)y + x(y+1) ISW (2xy+x+y)

I understand (a)(i) and (b)(i) since they are really obvious but the rest literally makes me want to strangle a new-born baby.

The question:

(a) An artist makes a sequence of patterns.He uses three types of metal pieces called rods, springs and bobs.He welds them together to make patterns.

In Pattern 2 there are 7 rods, 8 springs and 2 bobs.

In Pattern n there are n bobs.

(i) How many springs are there in Pattern n?

(ii) How many rods are there in Pattern n?

(b) The artist now changes his design to make new patterns with greater widths.The pattern below is called Pattern 3 by 2.In Pattern x by y there are xy bobs.

(i) How many springs are there in Pattern x by y?

(ii) How many rods are there in Pattern x by y?

The answer in accordance to the mark scheme:

(a) (i) 4n

(ii) 3n + 1

(b) (i) 4xy

(ii) Strategy,

e.g. simplify then extend or lookat vertical and horizontal Method leading to correct answer,

e.g. notices 1more row to dimension comparison (x+1)y + x(y+1) ISW (2xy+x+y)

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#2

(Original post by

I understand (a)(i) and (b)(i) since they are really obvious but the rest literally makes me want to strangle a new-born baby.

In Pattern 2 there are 7 rods, 8 springs and 2 bobs.

In Pattern n there are n bobs.

(i) How many springs are there in Pattern n?

(ii) How many rods are there in Pattern n?

(b) The artist now changes his design to make new patterns with greater widths.The pattern below is called Pattern 3 by 2.In Pattern x by y there are xy bobs.

(i) How many springs are there in Pattern x by y?

(ii) How many rods are there in Pattern x by y?

The answer in accordance to the mark scheme:

(a) (i) 4n

(ii) 3n + 1

(b) (i) 4xy

(ii) Strategy,

e.g. simplify then extend or lookat vertical and horizontal Method leading to correct answer,

e.g. notices 1more row to dimension comparison (x+1)y + x(y+1) ISW (2xy+x+y)

**utah**)I understand (a)(i) and (b)(i) since they are really obvious but the rest literally makes me want to strangle a new-born baby.

In Pattern 2 there are 7 rods, 8 springs and 2 bobs.

In Pattern n there are n bobs.

(i) How many springs are there in Pattern n?

(ii) How many rods are there in Pattern n?

(b) The artist now changes his design to make new patterns with greater widths.The pattern below is called Pattern 3 by 2.In Pattern x by y there are xy bobs.

(i) How many springs are there in Pattern x by y?

(ii) How many rods are there in Pattern x by y?

The answer in accordance to the mark scheme:

(a) (i) 4n

(ii) 3n + 1

(b) (i) 4xy

(ii) Strategy,

e.g. simplify then extend or lookat vertical and horizontal Method leading to correct answer,

e.g. notices 1more row to dimension comparison (x+1)y + x(y+1) ISW (2xy+x+y)

1st pattern and 2nd pattern using the 3n+1 nth term: ((3 * 1) + 1) = 4 and ((3 * 2) + 1) = 7

1st pattern and 2nd pattern using the 4n-1 nth term: ((4 * 1) - 1) = 3 and ((4 * 2) - 1) = 7

As you can see the numbers were different in the 1st pattern, as the '4n-1' nth term doesn't work.

So, if the current pattern is n. The number of bobs is equal to the pattern number.

So there are n bobs. Using the nth term rule, we can find out the number of springs & rods.

To work out the number of springs; we use: 4n. There is no number, therefore the answer is just 4n. It is the same with the rods, the answer is 3n+1.

You can use the same principle to work out the answer to (b)(i), as the number of bobs is equal to the pattern. If the pattern is x by y, the number of bobs is xy. Therefore, the number of springs will be 4xy, as the nth term is 4n.

I don't really understand (ii) myself, sorry.

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#3

I would say the question is a bit ambiguous, if they had given another set of numbers for another pattern, it would have helped.

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(Original post by

First of all, if it's the 2nd pattern, it's the 2nd term in the sequence. If there are 8 spring rolls, 8/2 = 4... so the nth term will be 4n. If there are 7 rods, it will be 3n+1 as 6+1=7. You could write 4n-1, but it won't work out for the rest of the terms. If you test it:

1st pattern and 2nd pattern using the 3n+1 nth term: ((3 * 1) + 1) = 4 and ((3 * 2) + 1) = 7

1st pattern and 2nd pattern using the 4n-1 nth term: ((4 * 1) - 1) = 3 and ((4 * 2) - 1) = 7

As you can see the numbers were different in the 1st pattern, as the '4n-1' nth term doesn't work.

So, if the current pattern is n. The number of bobs is equal to the pattern number.

So there are n bobs. Using the nth term rule, we can find out the number of springs & rods.

To work out the number of springs; we use: 4n. There is no number, therefore the answer is just 4n. It is the same with the rods, the answer is 3n+1.

You can use the same principle to work out the answer to (b)(i), as the number of bobs is equal to the pattern. If the pattern is x by y, the number of bobs is xy. Therefore, the number of springs will be 4xy, as the nth term is 4n.

I don't really understand (ii) myself, sorry.

**Chittesh14**)First of all, if it's the 2nd pattern, it's the 2nd term in the sequence. If there are 8 spring rolls, 8/2 = 4... so the nth term will be 4n. If there are 7 rods, it will be 3n+1 as 6+1=7. You could write 4n-1, but it won't work out for the rest of the terms. If you test it:

1st pattern and 2nd pattern using the 3n+1 nth term: ((3 * 1) + 1) = 4 and ((3 * 2) + 1) = 7

1st pattern and 2nd pattern using the 4n-1 nth term: ((4 * 1) - 1) = 3 and ((4 * 2) - 1) = 7

As you can see the numbers were different in the 1st pattern, as the '4n-1' nth term doesn't work.

So, if the current pattern is n. The number of bobs is equal to the pattern number.

So there are n bobs. Using the nth term rule, we can find out the number of springs & rods.

To work out the number of springs; we use: 4n. There is no number, therefore the answer is just 4n. It is the same with the rods, the answer is 3n+1.

You can use the same principle to work out the answer to (b)(i), as the number of bobs is equal to the pattern. If the pattern is x by y, the number of bobs is xy. Therefore, the number of springs will be 4xy, as the nth term is 4n.

I don't really understand (ii) myself, sorry.

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(Original post by

I would say the question is a bit ambiguous, if they had given another set of numbers for another pattern, it would have helped.

**simonli2575**)I would say the question is a bit ambiguous, if they had given another set of numbers for another pattern, it would have helped.

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#6

(Original post by

Yes indeed, it really would.

**utah**)Yes indeed, it really would.

A diagram perhaps?

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Here is the link(question 11):

http://www.jonesthesum.greenhill.pem...10_paper_1.pdf

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#8

(Original post by

Yes but it didn't offer much.

Here is the link(question 11):

http://www.jonesthesum.greenhill.pem...10_paper_1.pdf

**utah**)Yes but it didn't offer much.

Here is the link(question 11):

http://www.jonesthesum.greenhill.pem...10_paper_1.pdf

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(Original post by

The diagrams answer all your questions you have 3 sets of information for (a) and everything you need for (b)

**TenOfThem**)The diagrams answer all your questions you have 3 sets of information for (a) and everything you need for (b)

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#10

(Original post by

How do the diagrams give 3 sets of information? I cant see how the diagrams for each pattern give you the number of rods, springs and bobs present in each pattern.

**utah**)How do the diagrams give 3 sets of information? I cant see how the diagrams for each pattern give you the number of rods, springs and bobs present in each pattern.

Can you see where the 7 rods are, where the 8 springs are, and where the 2 bobs are

It should be obvious

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(Original post by

Look at the pattern for 2

Can you see where the 7 rods are, where the 8 springs are, and where the 2 bobs are

It should be obvious

**TenOfThem**)Look at the pattern for 2

Can you see where the 7 rods are, where the 8 springs are, and where the 2 bobs are

It should be obvious

And of course I suck.

Thanks a lot.

Oh can you explain how (b)(ii) is done? Just a little bit confused.

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#12

(Original post by

After a good 3 mins and 56 seconds of staring at it, I was able to see it.

And of course I suck.

Thanks a lot.

Oh can you explain how (b)(ii) is done? Just a little bit confused.

**utah**)After a good 3 mins and 56 seconds of staring at it, I was able to see it.

And of course I suck.

Thanks a lot.

Oh can you explain how (b)(ii) is done? Just a little bit confused.

You have the rules for 1by

Find the rules for 2by and 3by

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