Sequences & series

Edexcel Pure 4

A-level Maths (9MA0) · exam-style practice, examiner-report intelligence and the tools that drill it.

Board and spec code confirmed against Edexcel 9MA0 · registry checked 2026-07-11How this checking works

Edexcel 9MA0 revision notes Edexcel 9MA0 past papers

The topic on one screen

Geometric sequences: consecutive terms share a common ratio, so $(\text{2nd})^2 = \text{1st}\times\text{3rd}$ — the standard 'show that' opener.
A geometric series converges only when $|r| < 1$ ; then $S_\infty = \dfrac{a}{1 - r}$ . The condition is $|r| < 1$ , not 'it gets smaller'.
Arithmetic: $n$ th term $a + (n-1)d$ ; sum $S_n = \dfrac{n}{2}[2a + (n-1)d]$ . Write the formula before substituting.
Binomial expansion of $(1 + ax)^n$ : ${}^{n}C_{r}$ coefficients with the $a$ KEPT INSIDE the bracket power — $(ax)^r$ , not $ax^r$ .
For negative/fractional $n$ the expansion is only valid for $|ax| < 1$ — state the validity when asked.
Sigma notation is just a sum with a counter — write out the first few terms if the notation fogs you.

Where students actually lose marks

On the geometric 'show that' the scheme demands the given quadratic with no errors INCLUDING invisible brackets — $(12 - 3k)^2$ written without brackets kills the A* mark even if later work is right.

June 2023 Paper 1 mark scheme (Q09)

For convergence the scheme explicitly refuses 'the sequence is converging' as a reason — you must find $r$ and state $|r| < 1$ (with $r$ correct) to earn the mark.

June 2023 Paper 1 mark scheme (Q09)

In binomial expansions the scheme condones missing brackets around the x-term only if later work implies them — but the binomial coefficients must be correct, and wrong notation for ${}^{n}C_{r}$ is not allowed.

June 2024 Paper 1 mark scheme (Q02)

Try it — exam-style

Medium

ORIGINAL · after June 2023 Paper 1 Q09

The first three terms of a geometric sequence are

3k

k + 6

k + 2

, where

k

is a constant. Show that

k^2 - 3k - 18 = 0

(3)

(Total for Question 1 is 3 marks)

Medium

ORIGINAL · after June 2023 Paper 1 Q09

For the sequence above,

k = 6

gives terms 18, 12, 8, … Explain why the series converges and find its sum to infinity.

(3)

(Total for Question 2 is 3 marks)

Medium

ORIGINAL · after June 2024 Paper 1 Q02

Find, in ascending powers of

x

, the first four terms of the binomial expansion of

(1 + 2x)^8

, giving each term in simplest form.

(4)

(Total for Question 3 is 4 marks)

Easy

ORIGINAL

An arithmetic sequence has first term 5 and common difference 3. Find the sum of the first 20 terms.

(2)

(Total for Question 4 is 2 marks)

Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

Get the printable question packbrowser print view

Drill it properly

Formulae to Memorise

nth terms, sums and the binomial theorem on one page.

Maths flashcards

Sequence formulas and convergence conditions, drilled.

Mental Maths Trainer

The arithmetic speed that stops binomial slips.

Stuck on sequences & series?

'Invisible brackets' is the single most-cited error in these mark schemes — I train bracket discipline until it's automatic. Free intro call, then a free first lesson.

Book a free intro call