# Problem with sequences in practice paperWatch

#1
ZigZag Education Edexcel Practice GCSE Examination Paper Higher Set 3 Paper 2 Calculator Question 9b:

A different sequence contains four terms. The difference between each term is 8. The sum of all four terms is 4.
Write out the numbers in this sequence.
You must show all of your working. [3 marks]

I can get the solution by trial and error, but I don't know what working to show.
What's an algebraic proof for the question?

Thanks for any help anyone gives.
0
1 week ago
#2
You know the difference and the sum of the first 4 terms.
The only thing you don't know is the first value - so let that be the unknown.
Then write the other 3 items in the sequence in terms of this unknown, add them up and set equal to 4.
You have 1 equation in 1 unknown which you can solve.
1
1 week ago
#3
(Original post by lucaswinnerton)
ZigZag Education Edexcel Practice GCSE Examination Paper Higher Set 3 Paper 2 Calculator Question 9b:

A different sequence contains four terms. The difference between each term is 8. The sum of all four terms is 4.
Write out the numbers in this sequence.
You must show all of your working. [3 marks]

I can get the solution by trial and error, but I don't know what working to show.
What's an algebraic proof for the question?

Thanks for any help anyone gives.
You have four terms .

Let's say these go up in order, so we have .

You are told that the difference between each term is 8.

So , hence .
Similarly, hence
And so .

Adding them all up and equating this sum to 4 allows you to solve for and hence write out the leftover terms.

This can be done quicker if you're aware that the sum of an AP with terms and difference is given by . You are told and so you can solve for and then write down the leftover terms.
1
#4
(Original post by RDKGames)
You have four terms .

Let's say these go up in order, so we have .

You are told that the difference between each term is 8.

So , hence .
Similarly, hence
And so .

Adding them all up and equating this sum to 4 allows you to solve for and hence write out the leftover terms.

This can be done quicker if you're aware that the sum of an AP with terms and difference is given by . You are told and so you can solve for and then write down the leftover terms.
Thanks for the quick response! I wasn't sure what unknowns to use.
This method seems a little complicated for GCSE, but I'll bear it in mind. Thanks!
1
#5
(Original post by mqb2766)
You know the difference and the sum of the first 4 terms.
The only thing you don't know is the first value - so let that be the unknown.
Then write the other 3 items in the sequence in terms of this unknown, add them up and set equal to 4.
You have 1 equation in 1 unknown which you can solve.
That's great, thanks for your help!
0
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