Where can I download free nth term of a linear sequence PDF worksheets with answers?

On this MathsLinks page you can download free printable nth term of a linear sequence PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Ken Stafford (1), IGCSE MT, Maths Genie, Corbett Practice, plus a printable one-page nth term of a linear sequence revision guide.

What GCSE grade is nth term of a linear sequence (4H)?

nth term of a linear sequence (topic code 4H) is a Grade 4 algebra topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free nth term of a linear sequence Worksheets (PDF) with Answers — GCSE Maths

Free nth term of a linear sequence PDF Worksheets & Answers

Grade 4 • Topic 4H

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Ken Stafford (1) Practice worksheet & worked solutions	Qs	Ans
IGCSE MT IGCSE (9–1) past paper booklet	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
1st Class Maths (1) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (2) Edexcel exam questions & solutions	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
Dr Austin Practice grid / worksheet & answers	Qs	Ans
Maths4EveryOne KS2 SATs questions & solutions	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
Metatutor (1) Topic worksheet & worked solutions	Qs	Ans
GCSE Maths Rocket 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
MathsPad interactive resource Interactive online resource	Open
esheets Self-marking online worksheet	Page

Grade 4 topics
4A - Compound interest	4B - Indices (index laws)
4C - Prime factors HCF and LCM	4D - Real life graphs
4E - Inequalities on a number line	4F - Solving inequalities
4G - Forming and solving equations	4H - nth term of a linear sequence
4J - Expanding and factorising	4K - Pythagoras theorem
4L - Angles in parallel lines	4M - Angles in polygons
4N - Surface area	4P - Volume of a cuboid
4Q - Volume of a prism	4R - Bearings
4S - Cylinders	4T - Plans and elevations
4U - Scatter graphs	4V - Probability
4W - Averages from tables	4X - Reverse mean
4Y - Area of a trapezium	4Z - Loci and construction

Explanation:

To find the nth term of a linear (arithmetic) sequence, use the "DINO" method: find the common Difference d between terms and write dn, then find the 0th term (work backwards one step before the first term) and write it on the end.

To test whether a number is a term in the sequence, set the nth term equal to that number and solve for n. If n is a positive whole number (integer), then the number is in the sequence; if n is a fraction or decimal, it is not.

Example 1: Find the nth term and the 50th term of the sequence: 7, 11, 15, 19, 23, …

Solution:

Common difference = +4 → starts with 4n

0th term (before 7) = 7 − 4 = +3

nth term = 4n + 3

50th term (n = 50): 4(50) + 3 = 203

Answer: 4n + 3; 50th term = 203

Example 2: A sequence has nth term 6n − 5. Is 148 a term in this sequence? You must show your working.

Solution:

Set 6n − 5 = 148

6n = 153 → n = 153 ÷ 6 = 25.5

Since 25.5 is not a whole number (integer),

Answer: No, 148 is not in the sequence.

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper nth term of a linear sequence Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 OCR Nov 2024 2F Q8 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

(a) (i) A sequence is generated using the rule:
\textsf{multiply the previous term by } 3\textsf{, then subtract } 1.
The **2nd** term of the sequence is 20.
Find the **3rd** term of the sequence.
(ii) Find the **1st** term of the sequence.
(b) Here are the first four terms of a different sequence.
5 10 15 20
Find the nth term of the sequence.

(a) A sequence is generated using the rule:
\textsf{multiply the previous term by } 3\textsf{, then subtract } 1.
The **2nd** term of the sequence is 20.
Find the **3rd** term of the sequence. [1 mark]

Find the **1st** term of the sequence. [2 marks]

(b) Here are the first four terms of a different sequence.
5 10 15 20
Find the nth term of the sequence. [1 mark]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

20 × 3 − 1 = 59. B1

Answer (a): 59

Part Solution:

(20 + 1) ÷ 3 = 21 ÷ 3 = 7. M1 A1

Answer : 7

Part (b) Solution:

Multiples of 5 ⇒ nth term is 5n. B1

Answer (b): 5n n

Past Paper Example 2 IGCSE Jan 2019 1FR Q9 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here is a sequence of patterns made from white counters and black counters.

(a) In the space below, complete Pattern number 4 [1 mark]

(b) Find the total number of counters in Pattern number 6 [1 mark]

(d) Work out the total number of counters in Pattern number 50 [2 marks]

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

Pattern 4 drawn with 9 counters

Answer (a): Pattern 4 drawn with 9 counters

Part (b) Solution:

Answer (b): 13

Part (c) Solution:

Answer (c): 15

Part (d) Solution:

Pattern n has 2n + 1 counters M1
2 × 50 + 1 = 101 A1

Answer (d): 101

Past Paper Example 3 AQA Jun 2025 3F Q1 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here are the first three patterns in a sequence.

(a) Draw Pattern 4 on the grid. [1 mark]

(b) How many squares in Pattern 6 would have a cross (X) in them? [2 marks]

Worked Solution & Mark Scheme (3 marks)

Part (a) Solution:

Number of crosses follows the sequence: 5, 6, 7, 8, ..
Pattern 4 has 8 crosses (6 on top row, 2 on bottom row corners) B1

Answer (a): Pattern 4 drawn: top row of 6 crosses, bottom row with cross at left, cross at right, 4 shaded squares in between (total 8 crosses).

Part (b) Solution:

Pattern 1: 5 crosses, Pattern 2: 6 crosses, Pattern 3: 7 crosses, Pattern n: n + 4 crosses M1
For Pattern 6: 6 + 4 = 10 crosses A1

Answer (b): Answer 10

← 4G Forming and solving equations

Back to GCSE questions by topic

4J Expanding and factorising →