Problem with sequences in practice paper Watch

lucaswinnerton
Badges: 7
Rep:
?
#1
Report Thread starter 1 week ago
#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
reply
mqb2766
Badges: 12
Rep:
?
#2
Report 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
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#3
Report 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 a_1, a_2, a_3, a_4.

Let's say these go up in order, so we have a_1 < a_2 < a_3 < a_4.

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

So a_2 - a_1 = 8, hence a_2 = a_1 + 8.
Similarly, a_3 - a_2 = 8 hence a_3 = a_2 + 8 = (a_1 + 8) +8 = a_1 + 16
And so a_4 = a_1 + 24.

Adding them all up and equating this sum to 4 allows you to solve for a_1 and hence write out the leftover terms.


This can be done quicker if you're aware that the sum of an AP with n terms and difference d is given by S_n = \dfrac{n}{2}[2a_1 + (n-1)d]. You are told n,d and S_n so you can solve for a_1 and then write down the leftover terms.
1
reply
lucaswinnerton
Badges: 7
Rep:
?
#4
Report Thread starter 1 week ago
#4
(Original post by RDKGames)
You have four terms a_1, a_2, a_3, a_4.

Let's say these go up in order, so we have a_1 < a_2 < a_3 < a_4.

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

So a_2 - a_1 = 8, hence a_2 = a_1 + 8.
Similarly, a_3 - a_2 = 8 hence a_3 = a_2 + 8 = (a_1 + 8) +8 = a_1 + 16
And so a_4 = a_1 + 24.

Adding them all up and equating this sum to 4 allows you to solve for a_1 and hence write out the leftover terms.


This can be done quicker if you're aware that the sum of an AP with n terms and difference d is given by S_n = \dfrac{n}{2}[2a_1 + (n-1)d]. You are told n,d and S_n so you can solve for a_1 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
reply
lucaswinnerton
Badges: 7
Rep:
?
#5
Report Thread starter 1 week ago
#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
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • Solent University
    Postgraduate and Professional Open Evenings Postgraduate
    Mon, 25 Mar '19
  • Cardiff University
    Undergraduate Open Day Undergraduate
    Wed, 27 Mar '19
  • University of Portsmouth
    Postgraduate and Part-Time Open Evenings Postgraduate
    Wed, 27 Mar '19

Where do you need more help?

Which Uni should I go to? (149)
18.53%
How successful will I become if I take my planned subjects? (79)
9.83%
How happy will I be if I take this career? (136)
16.92%
How do I achieve my dream Uni placement? (114)
14.18%
What should I study to achieve my dream career? (79)
9.83%
How can I be the best version of myself? (247)
30.72%

Watched Threads

View All