Where can I download free quadratic sequences PDF worksheets with answers?

On this MathsLinks page you can download free printable quadratic sequences PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Ken Stafford (1), Maths Genie, Corbett Practice, Corbett Textbook, plus a printable one-page quadratic sequences revision guide.

What GCSE grade is quadratic sequences (8F)?

Quadratic sequences (topic code 8F) is a Grade 8+ algebra topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Quadratic sequences Worksheets (PDF) with Answers — GCSE Maths

Free Quadratic sequences PDF Worksheets & Answers

Grade 8+ • Topic 8F

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Ken Stafford (1) Practice worksheet & worked solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
Maths4EveryOne Structured worksheet & solutions	Qs	Ans
IGCSE MT IGCSE (9–1) past paper booklet	Qs	Ans
GCSE Maths Rocket (1) Practice questions & answers	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
Cognito Interactive online lesson & practice	Page
esheets Self-marking online worksheet	Page

Grade 8+ topics
8A - Quad. sim. equations	8B - Transforming graphs y=f(x)
8C - Algebraic proof	8D - Completing the square
8E - Quadratic inequalities	8F - Quadratic sequences
8G - Velocity time graphs	8H - Circles and tangents
8J - Circle theorem proof	8K - Vector proof
8L - Probability equation questions	8M - Invariant points
8N - Spheres, cones and cylinders	8P - Volume of a frustum

Explanation:

A quadratic sequence has nth term an² + bn + c and a constant second difference. Work out the first differences and second differences between terms, then halve the second difference to find a (since 2a = 2nd difference).

Write out the values of an² for n = 1, 2, 3, 4 and subtract them from the original sequence. The remaining numbers form a simple linear sequence bn + c; find its nth term and combine with an².

Example 1: Find the nth term of 4, 11, 22, 37, 56, ...

Solution:

1st diffs: +7, +11, +15, +19 ⇒ 2nd diff = +4

a = 4 ÷ 2 = 2, so sequence contains 2n²

Subtract 2n² (2, 8, 18, 32) from (4, 11, 22, 37):

Remainder sequence is 2, 3, 4, 5 ⇒ nth term is n + 1

Answer: 2n² + n + 1

Example 2: A sequence has nth term 3n² − 2n − 5. Is 128 a term in this sequence?

Solution:

Set 3n² − 2n − 5 = 128 ⇒ 3n² − 2n − 133 = 0

Factorise: (3n + 19)(n − 7) = 0

n = 7 or n = −193

Since n = 7 is a positive integer, 128 is the 7th term.

Answer: Yes, it is the 7th term (n = 7)

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Quadratic sequences Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 AQA Nov 2021 1H Q21 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

The first two terms of a quadratic sequence are 10 and 17
Here is some information about the sequence.

Work out an expression for the nth term of the sequence.

Worked Solution & Mark Scheme (4 marks)

Second difference is +6, so a = 62 = 3, giving 3n² M1
Comparing terms with 3n²:
n = 1: 10 - 3(1)² = 7 M1
n = 2: 17 - 3(2)² = 5
n = 3: 30 - 3(3)² = 3 M1
The sequence of differences 7, 5, 3, … has first difference -2, giving -2n + 9
Therefore, the nth term is 3n² - 2n + 9. A1

Answer: Answer 3n² - 2n + 9

Past Paper Example 2 OCR Nov 2022 4H Q18 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

Work out
(b) Here are the first four terms of a sequence.
1 √(3) 3 3√(3)
Write an expression for the nth term.
(c) Here are the first four terms of a quadratic sequence.
-1 5 13 23
The nth term is n² + bn + c.
Find the value of b and the value of c.

(b) Here are the first four terms of a sequence.
1 √(3) 3 3√(3)
Write an expression for the nth term. [2 marks]

(c) Here are the first four terms of a quadratic sequence.
-1 5 13 23
The nth term is n² + bn + c.
Find the value of b and the value of c. [3 marks]

Worked Solution & Mark Scheme (5 marks)

Part (b) Solution:

First term a = 1 = (√3)⁰, common ratio r = √3. M1
nth term = (√3) {}^n-1). A1

Answer (b): (√(3))^n-1

Part (c) Solution:

Subtract n² (1, 4, 9, 16) from the sequence (−1, 5, 13, 23): −2, 1, 4, 7. M1
This linear sequence has common difference 3 and nth term 3n − 5. M1
Therefore b = 3 and c = −5. A1

Answer (c): b = 3, c = −5

Past Paper Example 3 GCSE Nov 2024 2H Q15 6 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here are the first five terms of a quadratic sequence.
3 20 47 84 131

(a) Find an expression, in terms of n, for the nth term of this sequence. [3 marks]

(b) find the value of u₄ [3 marks]

Worked Solution & Mark Scheme (6 marks)

Part (a) Solution:

1st diffs: 17, 27, 37, 47 M1
2nd diff = 10 ⇒ 5n² M1
Subtracting 5n² gives –2, 0, 2, 4, 6 = 2n – 4 ⇒ 5n² + 2n – 4 A1

Answer (a): 5n² + 2n - 4

Part (b) Solution:

4 = 9k + k = 10k ⇒ k = 0.4 M1
u₃ = 0.4(4) + 0.4 = 2 M1
u₄ = 0.4(2) + 0.4 = 1.2 A1

Answer (b): u₄ = 1.2

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Quadratic sequences

Free Quadratic sequences PDF Worksheets & Answers

Guide to Quadratic sequences: Explanation, Diagrams & Worked Examples

GCSE Past Paper Quadratic sequences Questions & Answers