Sequences & series
A-level Maths (9MA0) · exam-style practice, examiner-report intelligence and the tools that drill it.
The topic on one screen
- Geometric sequences: consecutive terms share a common ratio, so (2nd)2 = 1st x 3rd — the standard 'show that' opener.
- A geometric series converges only when |r| < 1; then S∞ = a/(1 - r). The condition is |r| < 1, not 'it gets smaller'.
- Arithmetic: nth term a + (n-1)d; sum Sn = (n/2)[2a + (n-1)d]. Write the formula before substituting.
- Binomial expansion of (1 + ax)n: nCr coefficients with the a KEPT INSIDE the bracket power — (ax)r, not a xr.
- 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 nCr is not allowed.
June 2024 Paper 1 mark scheme (Q02)
Try it — exam-style
The first three terms of a geometric sequence are 3k, k + 6, k + 2, where k is a constant. Show that k2 - 3k - 18 = 0.
For the sequence above, k = 6 gives terms 18, 12, 8, … Explain why the series converges and find its sum to infinity.
Find, in ascending powers of x, the first four terms of the binomial expansion of (1 + 2x)8, giving each term in simplest form.
An arithmetic sequence has first term 5 and common difference 3. Find the sum of the first 20 terms.
Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.
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Stuck on sequences & series?
'Invisible brackets' is the single most-cited error in these mark schemes — I train bracket discipline until it's automatic, and your first lesson is free.