Prior Content: GCSE Sequences & Series
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Contents
- Whole Topic Notes
- 3A Arithmetic Sequences Introduction
- 3B Arithmetic Series
- 3C Geometric Sequences Introduction
- 3D Geometric Series
- 3E Geometric Sum to Infinity
- 3F Sigma Notation
- 3G Recurrence Relationships
- 3H Nature of Sequences
- 3I Sequences & Series in Context
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Download Full Topic Slides
- Textbook Notes as PPTs (Courtesy of Owen134866)
Full Notes to Accompany Slides
Dr Frost
- Dr Frost Sequences & Series Section
- Dr Frost Sequences & Series Slides✦
- Blank Notes to Follow Slides Word Doc or PDF (Courtesy of King’s Chester Maths Department)
Acute Learning Whole Chapter Problem Pairs
Activities
- Math = Love (Sarah Carter)
3A Arithmetic Sequences Introduction
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Dr Frost Video
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra 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 resources
Other Videos
Courtesy of Maths Genie
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- Berwick Maths Diagnostic Questions
- Goal Free Problems
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
- Dr Oliver Mathematics
- MadAsMaths (T. Madas)
- Arithmetic Series Exam Questions Q19, 99, 110 (difficulty 3–4 of 5)
Online Platforms
- Khan Academy
- Constructing arithmetic sequences: Videos & practice
3B Arithmetic Series
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Exam Practice
Extra 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)
Other resources
Other Videos
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
- NRICH
Worksheets
- Dr Austin Maths
- 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
- StudyWell
- 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)
Online Platforms
- Khan Academy
- Arithmetic series: Videos & practice
3C Geometric Sequences Introduction
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra 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 resources
Other Videos
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)
- Goal Free Problems
Online Platforms
- Khan Academy
- Constructing geometric sequences: Videos & practice
Worksheets
- martahidegkuti
- Dr Oliver Mathematics
- MadAsMaths (T. Madas)
- Geometric Series Q34, 36, 40, 47, 49–50, 54, 66, 72, 77, 90 (difficulty 3–5 of 5)
3D Geometric Series
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra 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 resources
Other Videos
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
- SRWhitehouse
- MathsPad
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
- 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)
Online Platforms
- Khan Academy
- Geometric series: Videos & practice
3E Geometric Sum to Infinity
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Exam Practice
Extra 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)
Other resources
Other Videos
Courtesy of Maths Genie (From 10:56)
Enrichment Video
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
- Goal Free Problems
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)
Online Platforms
- Khan Academy
- Infinite geometric series: Videos & practice
3F Sigma Notation
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Exam Practice
Extra 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
Other resources
Other Videos
Courtesy of Maths Genie
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- Berwick Maths Diagnostic Questions
- Transum
- Goal Free Problems
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)
Online Platforms
- Khan Academy
- Sigma (summation) notation: Videos & practice
3G Recurrence Relationships
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Exam Practice
Extra 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 xn+1 = f(xn)
Further Practice
Other resources
Other Videos
Courtesy of Maths Genie
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- Berwick Maths Diagnostic Questions
- Transum
- Goal Free Problems
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
- 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
Online Platforms
- Khan Academy
- General & recursive sequences: Videos & practice
3H Nature of Sequences
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Blank notes download
(Courtesy of King’s Chester Maths Department)
Download Slides
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 xn+1 = f(xn)
Further Practice
Other resources
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)
Activities
- eweston
- SRWhitehouse
3I Sequences & Series in Context
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra 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)
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- Berwick Maths Diagnostic Questions
- The Chalkface
- Goal Free Problems
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)
- 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)
Online Platforms
- Khan Academy
- Geometric series: Videos & practice
Whole Topic Summary Resources (Including Past Paper Questions)
Download PPQs as WW Powerpoint for A2 Sequences & Series
External Whole Topic Past Paper Style Questions
- Jethwa Maths Worksheets, Topic Tests and Starter Activities
- Dr Frost Topic Test✦ (Teacher Login Required)
- PMT
- AQA
- Edexcel
- Arithmetic Series
- General Sequences and Series 1 · 2
- Geometric Series 1 · 2
- OCR
- OCR MEI
- Cheat Sheet
- Susan Wall (Active A-level Maths)
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)
- NRICH (student problems)
- MEI
- Standards Unit
- Kangaroo Maths
- Andy Lutwyche
Worksheets
- Mathshelper (Jon Stone)
- MathedUp
- Maths Genie
- Sequences and Series: Questions · Solutions · Lesson · Topic page
- Jethwa Maths
- Year 2 Sequences and Series: Worksheets · Unit Test
- Mathsaurus (Kevin Olding)
- 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
- Dr Oliver Mathematics
- 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
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.