Sequences & Series

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A2 Maths – Pure – Arithmetic Sequences

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3A Slides (Courtesy of Owen134866)

Dr Frost Video

• KS 175 Determine the nth term formula of an arithmetic sequence

Bicen Maths Live Lesson

Sequences & Series 1 • Arithmetic Sequences • P2 Ex3A • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 1-11✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 573a: Determine the nth term formula for an arithmetic sequence with known first term and common difference.
• 573b: Determine the nth term formula for an arithmetic sequence given the first few terms.
• 573c: Determine a term of an arithmetic sequence with known first term and common difference.
• 573e: Determine the position of a term in an arithmetic sequence given the first term and common difference.
• 573f: Determine a term of an arithmetic sequence where the first term or constant difference is algebraic.
• 573g: Determine the first term and common difference of an arithmetic sequence given the position and value of two terms in the sequence.
• 573h: Determine the value of a given term in an arithmetic sequence given the position and value of two other terms in the sequence.
• 573i: Determine the position in two related sequences when there is a relationship between corresponding terms.
• 573j: Use the properties of an arithmetic sequence to determine an unknown constant in its terms.
• 573: Exam Practice: nth term formula for arithmetic sequences (using standard formulae)

Other Videos

Arithmetic Sequences

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Goal Free Problems
  • A-Level Sequences & Series set Q26

Worksheets

• Solomon C1 Worksheet A and Solutions A (Q1-3 only)
• Physics & Maths Tutor
  • Arithmetic Sequences: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• martahidegkuti
  • Arithmetic sequences practice problems✦
• Dr Oliver Mathematics
  • Arithmetic sequences questions✦ (solutions✦)
• MadAsMaths (T. Madas)
  • Arithmetic Series Exam Questions Q19, 99, 110 (difficulty 3–4 of 5)

A2 Maths – Pure – Arithmetic Series

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3B Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Sequences & Series 2 • Arithmetic Series • P2 Ex3B • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 12-19✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 574a: Prove the formula for the sum of the first n terms of an arithmetic series.
• 574b: Find the sum of the first n terms (the nth partial sum) of an arithmetic series.
• 574d: Determine the sum of multiples in a given range.
• 574e: Determine the sum of terms in an arithmetic series in-between two given terms.
• 574f: Determine the sum of terms in an arithmetic series where the number of terms must be determined.
• 574g: Find the number of terms for an arithmetic series to equal a given value.
• 574h: Find the least number of terms for an arithmetic series to exceed a given value.
• 574i: Determine the sum of terms in an arithmetic series where the terms are algebraic expressions.
• 574l: Determine the first term and common difference for an arithmetic series given the value of a term and a sum of terms.
• 574m: Determine the value of a given term in an arithmetic series using the value of another term and a sum of terms.
• 574n: Reason about a sum of terms in an arithmetic sequence given another sum of its terms.
• 574o: Determine the first term and common difference for an arithmetic series given two sums of terms.
• 574p: Use the properties of an arithmetic sequence to determine an unknown constant in its terms.
• 574: Exam Practice: Sum terms in an arithmetic series

Further Practice (all things Arithmetic)

• Practise Questions

Other Videos

Arithmetic Series

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• The Chalkface
  • Money Matters: PDF
• Goal Free Problems
  • A-Level Sequences & Series set Q3, Q4, Q24, Q25
• NRICH
  • AP sum proof sorter✦

Worksheets

• Dr Austin Maths
  • Sum of an Fill in the Blanks (Word | PDF | Answers)
  • Sum of an Practice Strips (Word | PDF | Answers)
  • Harder Sum Fill in the Blanks (Word | PDF | Answers)
  • Revision Practice Grid (Word | PDF | Answers)
• Jethwa Maths
  • Worksheet (Part 2)
  • Topic Test (p4-7)
• Solomon C1
  • Worksheet B and Solutions B (Not Q13&14)
  • Worksheet C and Solutions C (Not Q5)
• SRWhitehouse
  • Arithmetic series worksheets✦ (questions✦)
• StudyWell
  • Arithmetic series exam questions with solutions✦
• MadAsMaths (T. Madas)
  • Arithmetic Series Exam Questions Q1–3, 7–12, 14, 16, 18, 20–27, 29–34, 38, 41, 43–46, 48, 50, 56, 60, 62, 64, 66, 69, 71–72, 74–75, 77–81, 83, 86–87, 90, 94, 96–98, 100, 104–107, 111, 113–114, 118–125, 128 (difficulty 2–5 of 5)

A2 Maths – Pure – Geometric Sequences

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3C Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Sequences & Series 3 • Geometric Sequences • P2 Ex3C • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost slides 20-27✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 575a: Determine a term of a geometric sequence given the first term and common ratio.
• 575c: Determine the first term and common ratio of a geometric sequence given two terms in the sequence.
• 575d: Determine the value of a term in a geometric sequence given two terms in the sequence.
• 575e: Use the properties of a geometric sequence to determine an unknown constant in its terms.
• 575f: Determine the first term of a geometric sequence to exceed a value.
• 203o: Determine a later term in a geometric sequence.
• 575: Exam Practice: nth term formula for a geometric sequence (using standard formulae)

Other Videos

Geometric Sequences

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Don Steward Median✦
• Math = Love (Sarah Carter)
  • Geometric Formula Organiser
• Goal Free Problems
  • A-Level Sequences & Series set Q16

A2 Maths – Pure – Geometric Series

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3D Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Sequences & Series 4 • Geometric Series • P2 Ex3D • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 28-32✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 578a: Prove the formula for the sum of the first n terms of a finite geometric series.
• 578b: Find the sum of the first n terms (the nth partial sum) of a geometric series.
• 578e: Determine the least number of terms for a geometric series to exceed or equal a given value.
• 578j: Deal with geometric series involving logarithmic terms.
• 578: Exam Practice: Summing terms in a geometric series (including the sum to infinity)

Other Videos

Geometric Series

Courtesy of Maths Genie (up to 10:56)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Goal Free Problems
  • A-Level Sequences & Series set Q20, Q21
• SRWhitehouse
  • Geometric series activities✦ (questions✦)
• MathsPad
  • To Sum Up✦

Worksheets

• Solomon C2 Worksheet A and Solutions A (Not Q5 or13 onwards)
• Physics & Maths Tutor
  • Geometric Series: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• StudyWell
  • Geometric series exam questions with solutions✦
• MadAsMaths (T. Madas)
  • Geometric Series Q1, 4, 6, 16–20, 29, 33, 52, 55, 63, 65, 70, 79–80, 82 (difficulty 2–4 of 5)
  • Series Mixed Exam Questions Q21 (difficulty 5 of 5)
  • Trigonometry Exam Questions Enrichment Questions Q64 (difficulty 5 of 5)

A2 Maths – Pure – Geometric Sum to Infinity

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3E Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Sequences & Series 5 • Sum to Infinity • P2 Ex3E • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 33-38✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 578f: Determine the sum to infinity of a geometric series.
• 578g: Determine the first term or common ratio of a series given its sum to infinity.
• 578h: Determine a term or common ratio in a geometric series given a ratio between either the sum of terms or sum to infinity, and a term or sum of terms in the sequence.
• 578i: Determine the first term or common ratio when the sum to infinity and a sum of terms is given.
• 578: Exam Practice: Summing terms in a geometric series (including the sum to infinity)

Further Practice (everything Geometric)

• Practise Questions

Other Videos

Geometric Series

Courtesy of Maths Genie (From 10:56)

Enrichment Video

Zeno's Paradox – Numberphile

Numberphile: Zeno's Paradox

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Geometric Race by Ms Steel (TES)
• The Chalkface
  • Zeno's Paradoxes: PDF
  • Gender Balance: PDF
• Goal Free Problems
  • A-Level Sequences & Series set Q17, Q18, Q22, Q30

Worksheets

• Jethwa Maths Worksheet (Part 3)
• Jethwa Maths, Topic Test (p8-11)
• Solomon C2 Worksheet A and Solutions A (Not Q5)
• Solomon C2 Worksheet B and Solutions B (Not Q9)
• MadAsMaths (T. Madas)
  • Geometric Series Q2–3, 5, 8–13, 15, 21–23, 26–27, 30–32, 35, 37–38, 42, 44–46, 51, 53, 57–62, 69, 71, 73, 84, 86, 92, 97–101, 106, 110 (difficulty 2–5 of 5)
  • Series Mixed Exam Questions Q6–7, 13 (difficulty 4 of 5)
  • Calculus Introduction Exam Questions Q305 (difficulty 5 of 5)
  • Trigonometry Exam Questions Hard Questions Q39 (difficulty 4 of 5)

A2 Maths – Pure – Sigma Notation

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3F Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Sequences & Series 6 • Sigma Notation • P2 Ex3F • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 39-43✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 581a: Determine the first term and common difference/ratio in an arithmetic or geometric series expressed using sigma notation.
• 581b: Determine the sum of terms of an arithmetic sequence expressed using sigma notation.
• 581c: Determine the sum of terms of a geometric series expressed using sigma notation.
• 581d: Determine the sum to infinity of a geometric series expressed using sigma notation.
• 581e: Determine a sum of a mixture of an arithmetic and geometric series using sigma notation.
• 581f: Determine the sum of terms of a geometric series, expressed using sigma notation, when the terms are logarithmic.
• 581: Exam Practice: Sigma notation for sums of series

Further Practice

• Practise Questions

Other Videos

Arithmetic Series Sigma Notation

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Transum
  • Sigma
• Goal Free Problems
  • A-Level Sequences & Series set Q12, Q13

Worksheets

• Solomon C1 Worksheet B and Solutions B (Q13&14 only)
• Solomon C1 Worksheet C and Solutions C (Q5)
• Solomon C2 Worksheet A and Solutions A (Q5)
• Solomon C2 Worksheet B and Solutions B (Q9)
• MadAsMaths (T. Madas)
  • Arithmetic Series Exam Questions Q4–5, 13, 15, 36, 42, 49, 52, 55, 57, 59, 63, 67–68, 73, 82, 84, 101, 115–117, 126 (difficulty 2–5 of 5)
  • Geometric Series Q7, 24, 68, 75, 85, 88, 93, 96 (difficulty 2–5 of 5)
  • Series Mixed Exam Questions Q8, 11–12, 18–20, 24 (difficulty 4–5 of 5)

A2 Maths – Pure – Recurrence Relations

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3G Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Sequences & Series 7 • Recurrence Relations • P2 Ex3G • 🎲

Sequences & Series 8 • Sigma and Recurrence exam questions • P2 Ex3 ExamQ • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 44-49✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 582b: Use a recurrence relation and the first term to find subsequent terms of a sequence.
• 582c: Identify the type of sequence given a term-to-term recurrence or position-to-term formula.
• 582e: Use a recurrence relation involving two previous terms to find a subsequent term or a sum of terms.
• 582f: Use a recurrence relation, involving an algebraic constant, and the first term to find subsequent terms of a sequence.
• 582g: Use known consecutive terms of a sequence and a recurrence relation to find values of a constant.
• 582h: Use known non-consecutive terms of a sequence and a recurrence relation to find values of a constant.
• 582j: Use sigma notation combined with a recurrence relation to find values of a constant.
• 582l: Determine the limiting value of a convergent recurrence relation.
• 582: Exam Practice: Recurrence relations given in the form x_n+1 = f(x_n)

Further Practice

• Practise Questions

Other Videos

Recurrence Relations

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Transum
  • Term-To-Term
• Goal Free Problems
  • A-Level Sequences & Series set Q11, Q14, Q15, Q28

Worksheets

• Jethwa Maths Worksheet (Part 4)
• Jethwa Maths, Topic Test (p12-14)
• Solomon C1 Worksheet A and Solutions A (Q4 onwards)
• Chuckierish ✦on TES
• Naiker Maths
  • Sigma Notation & Recurrence Relations: Exam Qs 2005–11 · Mark scheme · Exam Qs 2012–17 · Mark scheme
• StudyWell
  • Recurrence relations exam questions with solutions✦
• MadAsMaths (T. Madas)
  • Recurrence Relations Q1–3, 5–13, 15–33, 35, 37–38, 40–42, 47–48, 52–57, 59–60 (difficulty 2–4 of 5)
• Starting Points Maths
  • Recurrence Relations · PDF

A2 Maths – Pure – Types of Sequences

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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3H Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Sequences & Series 9 • Increasing, Decreasing, Periodic • P2 Ex3H • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Blank notes download

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 50-52✦

Extra Questions

• Dr Frost Questions (very short and final 2 Qs from MAT)

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 582a: Identify whether a sequence is arithmetic, geometric or periodic given its terms.
• 582d: Determine the order of a periodic sequence using a recurrence relation.
• 582i: Use the periodicity of a sequence combined with a recurrence relation to form and solve an equation.
• 582k: Determine the sum of a large number of terms of a periodic sequence.
• 582m: Use a periodic sequence, defined by a recurrence relation, to determine a distant term in the sequence.
• 582n: Prove algebraically that a sequence, defined using a recurrence relation, is periodic for any starting value.
• 582: Exam Practice: Recurrence relations given in the form x_n+1 = f(x_n)

Further Practice

• Practise Questions

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Jethwa Maths Worksheets (Part 4 Q5-8)
• MadAsMaths (T. Madas)
  • Recurrence Relations Q4, 14, 34, 43–44, 49–51, 62, 64–65 (difficulty 2–5 of 5)
  • Series Mixed Exam Questions Q26 (difficulty 5 of 5)

A2 Maths – Pure – Modelling with Series

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

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3I Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Sequences & Series 10 • Modelling and Exam Questions • P2 Ex3I • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 53-58✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 573d: Determine a term of an arithmetic sequence used to model a given context.
• 574c: Find the sum of the first n terms of an arithmetic series used to model a given context.
• 574j: Solve problems involving comparison of two arithmetic sequences.
• 574k: Determine the sum of terms in an arithmetic series where terms are eventually capped at an amount.
• 575b: Determine a term of a geometric sequence used to model a given context.
• 578c: Determine the sum of terms in a geometric series used to model a given non-financial context.
• 578d: Determine the sum of terms in a geometric series used to model a given financial context.
• 573: Exam Practice: nth term formula for arithmetic sequences (using standard formulae)
• 574: Exam Practice: Sum terms in an arithmetic series
• 575: Exam Practice: nth term formula for a geometric sequence (using standard formulae)
• 578: Exam Practice: Summing terms in a geometric series (including the sum to infinity)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• The Chalkface
  • Buffer: Excel (if macros are blocked: right-click the file › Properties › tick Unblock)
  • Superman Bleep Test: PDF
• Goal Free Problems
  • A-Level Sequences & Series set Q1, Q2, Q5, Q19, Q23, Q29

Worksheets

• Jethwa Maths Worksheets, Topic Tests
• Solomon C1 Worksheet C and Solutions C (Q6 & 12)
• Solomon C2 Worksheet B and Solutions B (Q7 & 15)
• Mathshelper (Jon Stone)
  • Mortgage Repayment Formula Derivation
• Naiker Maths
  • Modelling with Series: Exam Qs 2005–11✦ · Mark scheme✦ · Exam Qs 2012–17 · Mark scheme
• MadAsMaths (T. Madas)
  • Arithmetic Series Exam Questions Q6, 17, 28, 35, 37, 39–40, 47, 51, 53–54, 58, 61, 65, 70, 76, 85, 88–89, 91–93, 95, 102, 108–109, 112 (difficulty 2–4 of 5)
  • Arithmetic Series Worded Questions Q1–27 (difficulty 2–4 of 5)
  • Geometric Series Q14, 25, 28, 39, 41, 43, 48, 56, 64, 67, 74, 76, 78, 81, 83, 87, 89, 94, 107, 111 (difficulty 2–5 of 5)
  • Geometric Series Worded Questions Q1–19 (difficulty 2–5 of 5)
  • Recurrence Relations Q45–46, 63 (difficulty 4–5 of 5)
  • Series Mixed Exam Questions Q23 (difficulty 5 of 5)

External Whole Topic Past Paper Style Questions

• Jethwa Maths Worksheets, Topic Tests and Starter Activities
• Dr Frost Topic Test✦ (Teacher Login Required)
• PMT
  • AQA
    • Sequences & Series
  • Edexcel
    • Arithmetic Series
    • General Sequences and Series 1 · 2
    • Geometric Series 1 · 2
  • OCR
    • Arithmetic Sequences
    • Geometric Sequences
    • Sigma Notation
  • OCR MEI
    • Arithmetic Series
    • Geometric Series
    • Sequences
  • Cheat Sheet
• Susan Wall (Active A-level Maths)
  • Sequences and Series: Introduction · Matching sequences · APs and GPs · Which belongs to which? · Sorting sequences (Susan Wall;

Other Whole Topic Resources

• MEI Thinking About Series✦
• Underground Maths:
  • Sort it out✦, 
  • Can You Find… Series Edition✦, 
  • Common Terms✦, 
  • Change One Thing✦, 
  • Connect Three?✦, 
  • Same or Different?✦ Credit to Resourceaholic for finding these

Activities

• Math = Love (Sarah Carter)
  • Sequences & Series activities
• NRICH (student problems)
  • Sequences & Series
• MEI
  • MEI teaching notes, misconceptions & prompts: Sequences and series✦
• Standards Unit
  • Analysing sequences✦
• Kangaroo Maths
  • Kangaroo lovers✦
• Andy Lutwyche
  • Erica’s Errors

Worksheets

• Mathshelper (Jon Stone)
  • Sequences & Series
  • Sequences
• MathedUp
  • Sequences and series: Questions · Challenge · Answers
• Maths Genie
  • Sequences and Series: Questions · Solutions · Lesson · Topic page
• Jethwa Maths
  • Year 2 Sequences and Series: Worksheets · Unit Test
• Mathsaurus (Kevin Olding)
  • Sequences and series (exam questions)
• Naiker Maths
  • Sequences & Series: Exam Qs 2005–11✦ · Mark scheme✦ · Exam Qs 2012–17 · Mark scheme
• Physics & Maths Tutor
  • Sequences and Series: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MME
  • C1 Sequences: Questions | Answers  •  C2 Sequences & Series: Questions | Answers
• Dr Oliver Mathematics
  • Sequences questions✦ (solutions✦)
• MadAsMaths (T. Madas)
  • Arithmetic Series Exam Questions Q103, 127 (difficulty 4–5 of 5)
  • Geometric Series Q91, 95, 103 (difficulty 5 of 5)
  • Series Mixed Exam Questions Q1–5, 9–10, 14–16, 22 (difficulty 3–5 of 5)
• Dr Austin Maths
  • Revision Practice Grid (Word | PDF | Answers)