Edexcel Pure Paper 2 2024 Question 2 Solution

Edexcel Pure Paper 2 2024 Question 2 – Arithmetic Sequences and Totals

❓ The Question

🧠 Before you start

At the beginning, this just looks like a standard sequence question.

First term, common difference — nothing unusual there. Most people are fine up to that point.

Where it shifts slightly is when the question starts talking about the total amount repaid. That’s where a few people keep going with the same approach, even though it doesn’t really fit anymore.

So the main thing here is spotting that change early. Once you do, the rest is fairly routine.

✏️ Working

Part (a)

Start with the usual setup.

You’ve got an arithmetic sequence, so:

$u_n = a + (n-1)d$

From the question, the first payment is $400$ , and it drops by 10 each time. So:

$a = 400, \quad d = -10$

Put that into the formula:

$u_n = 400 + (n-1)(-10)$

Now take the 12th term.

$u_{12} = 400 + 11(-10)$

That gives:

$u_{12} = 400 – 110 = 290$

That’s all part (a) was after.

Part (b)

This is where things change a bit.

We’re no longer looking for a single term — it’s the total amount repaid. So now we need the sum.

Use:

$S_n = \frac{n}{2}(2a + (n-1)d)$

Substitute what we know:

$S_n = \frac{n}{2}(800 – 10(n-1))$

You can tidy that up first if you want:

$800 - 10(n-1) = 810 - 10n$

So:

$S_n = \frac{n}{2}(810 – 10n)$

Now set it equal to the total loan:

$\frac{n}{2}(810 – 10n) = 8100$

Multiply through:

$n(810 - 10n) = 16200$

Then expand:

$810n - 10n^2 = 16200$

Rearrange it:

$10n^2 - 810n + 16200 = 0$

And divide by 10:

$n^2 - 81n + 1620 = 0$

Part (c)

Now just solve that.

$n^2 - 81n + 1620 = 0$

It factorises quite neatly:

$(n - 36)(n - 45) = 0$

So you get:

$n = 36 \quad \text{or} \quad n = 45$

At this point, it’s not just about solving the equation — you need to think about the situation.

The payments are getting smaller each month. If you carry on too long, eventually you’d hit zero and then go negative, which doesn’t really make sense here.

So the valid answer is:

$n = 36$

🎯 Where the Marks Are

Nothing unusual here.

Part (a) is just using the nth term properly.
Part (b) is recognising it’s a sum, not a term — that’s the key step.
Part (c) is straightforward once the equation is right.

If part (b) goes wrong, everything after it usually does too.

⚠️ What Went Wrong

Most of the issues came from using the wrong idea at the wrong time.

Some answers stuck with $u_n$ in part (b), even though the question had clearly moved on to totals.

There were also a few algebra slips when expanding brackets. Not major ones — just enough to throw off the quadratic.

And in part (c), a few people listed both solutions without checking which one actually made sense.

That last step is easy to skip if you’re just focused on finishing.

💡 One Small Tip

If a question suddenly talks about “total” or “amount repaid”, stop and check what you’re using.

That’s usually your signal that you need a sum, not a term.

🚀 If This Felt Difficult

If this didn’t feel that smooth, it’s often because sequences and algebra aren’t quite linking up yet.

Working through more questions like this is one of the best ways to prepare for A level maths exams, especially since they tend to appear in slightly different forms each year.

And if the algebra side is where things get messy, getting some focused help understanding maths can make these feel much more straightforward.

🔗 Next Steps

← Question 1 Solution
→ Question 3 Solution

👨‍🏫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 switch to the sum formula?

Because you’re dealing with the total, not a single term anymore.

📌Do both solutions work?

No — only one fits the context of the question.

📌Is factorising expected?

Yes, if the quadratic is straightforward like this.

📌Is this a common exam style?

Very — sequences leading into algebra comes up a lot.