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Edexcel Pure Paper 2 2024 Question 4
Edexcel Pure Paper 2 2024 Question 4 – Sequences and Algebra
❓ The Question
🧠 Before you start
This one can feel slightly unusual at first.
It’s still a sequence, but it’s written in a way that isn’t as familiar as a standard arithmetic or geometric form. That’s usually what slows people down — not the difficulty, just the way it’s presented.
The key thing is not to panic and try to force a method straight away. Instead, take a moment to see how each term is built from the previous one.
Once that part is clear, everything else tends to follow quite naturally.
✏️ Working
We’re given a recursive relationship:
u_{n+1} = k u_n – \frac{5}{u_n}
and told that u_3 = -1.
So rather than jumping ahead, it makes sense to work through the terms step by step.
Part (a)
The goal here is to show a relationship involving k.
To do that, we need expressions for u_2 and u_3.
Start with u_1, then build forward.
First:
u_2 = k u_1 – \frac{5}{u_1}
Then:
u_3 = k u_2 – \frac{5}{u_2}
Now substitute the expression for u_2 into the equation for u_3.
This step can get messy if rushed, so it’s worth writing it out carefully rather than trying to do it mentally.
Once you substitute and simplify — and this does take a bit of patience — everything reduces down to an equation in k.
You should end up with:
6k^2 – 5k – 4 = 0
That’s what the question is guiding you towards.
Part (b)(i)
Now we solve that quadratic.
6k^2 – 5k – 4 = 0
Factorising:
(3k + 2)(2k – 2) = 0
So:
k = -\frac{2}{3} \quad \text{or} \quad k = 1
Both values come from the algebra, so at this stage they’re both valid mathematically.
Part (b)(ii)
Now we use the correct value of k to find the required term.
This is where you need to think slightly about the sequence itself.
Depending on the context of the question, one value of k may lead to behaviour that doesn’t fit what’s expected (for example, values that don’t match the given condition).
Once the appropriate value is chosen, you can substitute it back into the recurrence relation and work forward to find the required term.
It’s not particularly complicated at this stage — just careful substitution and keeping track of each step.
🎯 Where the Marks Are
Most of the marks are in part (a).
Not because the maths is harder, but because it’s easy to lose track of the algebra if it isn’t written clearly.
The remaining marks come from solving the quadratic and then using the correct value of k.
So overall, it’s more about organisation than anything else.
⚠️ What Went Wrong
This question wasn’t necessarily difficult, but it did catch people out.
A common issue was trying to skip steps when substituting into u_3. That usually led to expressions that didn’t simplify properly.
Another problem was algebra errors — especially when dealing with fractions. Once something small goes wrong there, the final equation doesn’t come out correctly.
Some answers also stopped after finding both values of k, without considering which one actually works in the sequence.
💡 One Small Tip
If a sequence is defined recursively like this, don’t try to jump straight to a formula.
Work through it step by step instead. It might feel slower, but it keeps everything much clearer.
🚀 If This Felt Difficult
If this felt a bit unfamiliar, that’s usually because recursive sequences don’t come up as often in simple forms.
They’re still a regular part of exams though, so it’s worth spending time on them.
Working through similar problems can really help you get help with maths questions like this, especially where algebra and sequences are combined.
And if you’re aiming to feel confident across all of these topics, taking the time to properly master A level maths content makes a big difference when questions start to mix ideas together.
🔗 Next Steps
👨🏫Author Bio
S Mahandru is an A Level Maths teacher focused on helping students stay accurate under exam pressure. The aim is to keep methods clear and build confidence through consistent exam-style practice.
❓ Frequently Asked Questions
📌Why substitute step by step?
Because trying to do everything at once usually leads to mistakes.
📌Do both values of k always work?
Not necessarily — you need to check what fits the sequence.
📌Is this a standard type of question?
It’s not the most common, but it does appear regularly enough to be important.
📌What’s the main difficulty here?
Keeping the algebra organised while working through the recurrence.