Prior Content: Solving Simple Equations, Substitution, Simultaneous Equations, Solving Quadratics
Possible Next Steps: Iterations, Properties of Numbers, Percentages
Contents
- 1.1 Noticing Patterns & Predicting Next Terms
- 1.2 Using nth Terms
- 2.1 Arithmetic Sequences: Finding Next Terms
- 2.2 Arithmetic Sequences: Finding & Using nth Terms
- 2.3 Arithmetic Sequences: nth Term Formulae
- 2.4 Arithmetic Series
- 3.1 Geometric Sequences
- 4.1 Other Famous & Recognisable Sequences
- 5.1 Quadratic Sequences: Recognising & Finding Next Terms
- 5.2 Quadratic Sequences: Finding nth Terms
- 6.1 Limit of a Sequence (AQA Level 2)
- Whole Topic Summary Resources (Including Past Paper Questions)
1.1 Noticing Patterns & Predicting Next Terms
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Sequences: Describing Rules
Corbett Maths Sequences: Missing Terms
Corbet Maths Sequences: Patterns
Online Platforms (with Videos & Exercises)
Activities & Resources
- Maths 4 Everyone
- Pixi Maths
Worksheets
- Dr Austin Maths
- Patterns and Sequences Practice Strips (Editable Word | PDF | Answers)
- Continuing Sequences Fill In The Blanks (Editable Word | PDF | Answers)
- Corbettmaths
- Sequences Practice Questions & Solutions
- Sequences Missing Terms Worksheet & Solutions
- Patterns Practice Questions & Solutions
- Patterns Worksheet & Solutions
- Pixi Maths
Dr Frost Resources
Dr Frost Video
K158: Continue a Sequence.
Dr Frost Slides & Activities
- All in one summary sheet
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
- 203a: Describe the term-to-term rule of a sequence.
- 203b: Draw the next term in a pictorial sequence.
- 203c: Draw a later term in a pictorial sequence.
- 203d: Determine the number of items (e.g. squares) in a subsequent shape, following an arithmetic sequence.
- 203h: Generate a sequence using a rule involving two arithmetic operations.
- 203: Exam Practice: Describing, generating and continuing sequences using term-to-term rules
Extension Materials
1.2 Using nth Terms
Teaching Videos, Exercises & Activities
Tutorial Videos
Online Platforms (with Videos & Exercises)
Activities & Resources
Worksheets
- Dr Austin Maths
- Generating Sequences Practice Strips (Editable Word | PDF | Answers)
- Generating Sequences Match-Up (Editable Word | PDF | Answers)
- Corbettmaths
- nth Terms AQA Level 2 Practice Questions & Solutions
- Maths 4 Everyone
- Pixi Maths
Dr Frost Resources
Dr Frost Video
K163: Generate Terms in a Sequence Using a Linear nth Term.
K164: Generate Terms in a Sequence Using a Non-Linear nth Term.
Dr Frost Slides & Activities
- Dr Frost Slides (4)
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 204a: Generate any term in a sequence using a linear nth term.
- 204b: Generate the first few terms of a sequence given a linear nth term.
- 204c: Generate terms in a sequence using a quadratic nth term.
- 204d: Generate terms in a sequence using a geometric nth term.
- 204e: Generate terms in a sequence using an nth term with brackets or powers greater than 2.
- 204f: Generate terms in a sequence using a fractional nth term.
- 204: Exam Practice: Generating terms of a sequence given a position-to-term rule
Extension Materials
2.1 Arithmetic Sequences: Finding Next Terms
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Online Platforms (with Videos & Exercises)
Activities & Resources
Worksheets
- Maths 4 Everyone
Dr Frost resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
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
- 203e: Generate an arithmetic sequence given the first term and the common difference.
- 203i: Determine the next term(s) in an arithmetic sequence.
- 203m: Determine a later term in an arithmetic sequence.
- 203p: Determine missing terms in an arithmetic sequence where two consecutive terms are given.
- 203q: Determine missing terms in an arithmetic sequence where two consecutive terms are not given.
- 203r: Determine the difference between non-consecutive terms of an arithmetic sequence.
- 203u: Continue an arithmetic sequence where terms are algebraic.
- 203: Exam Practice: Describing, generating and continuing sequences using term-to-term rules
Further Practice
- Practise Questions (may include angles in a triangle and on a straight line)
EXTENSION MATERIALS
2.2 Arithmetic Sequences: Finding & Using nth Terms
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths The nth Term
Corbett Maths nth Term for Fractional Sequences
Online Platforms (with Videos & Exercises)
Activities
- Maths 4 Everyone
- maths box Finding the nth term (linear sequences) treasure hunt (free sample activity)
- Pixi Maths
Worksheets
- Dr Austin Maths
- Nth Term of a Linear Sequence Practice Strips (Editable Word | PDF | Answers)
- Nth Term of a Linear Sequence Decode the Joke (Editable Word | PDF | Answers)
- Nth Term of an Ascending Linear Sequence Fill In The Blanks (Editable Word | PDF | Answers)
- Nth Term of a Descending Linear Sequence Fill In The Blanks (Editable Word | PDF | Answers)
- Using the Nth Term of a Linear Sequence Practice Strips (Editable Word | PDF | Answers)
- Linear Sequences Fill In The Blanks (Editable Word | PDF | Answers)
- Corbettmaths
- nth Term Practice Questions & Solutions
- nth Term Worksheet & Solutions
- Maths 4 Everyone
- Pixi Maths
Dr Frost resources
Dr Frost Video
K163: Generate Terms in a Sequence Using a Linear nth Term.
K160: Determine the nth Term Formula of an Ascending Arithmetic Sequence.
K161: Determine the nth Term Formula of a Descending Arithmetic Sequence.
K162: Determine Whether a Number is a Term in an Arithmetic Sequence.
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
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
- 205a: Determine the nth term formula for an arithmetic sequence by comparison to an
- 205b: Determine the nth term formula for an ascending arithmetic sequence.
- 205c: Determine the nth term formula for a descending arithmetic sequence.
- 205d: Determine the nth term formula for shapes in a sequence.
- 205e: Determine the nth term for an arithmetic sequence with fractional terms.
- 205f: Determine the nth term formula for an ascending arithmetic sequence where n is algebraic.
- 205g: Use an existing formula for an arithmetic sequence to determine the formula for a similar sequence.
- 205h: Determine the formula for an arithmetic sequence given non-consecutive terms.
- 206a: Determine whether a number is a term in an arithmetic sequence using properties such as evenness/oddness.
- 206b: Determine whether a number is a term in an arithmetic sequence by continuing the sequence.
- 206c: Determine whether a number is a term in an arithmetic sequence using algebra.
- 206d: Determine the term number of a particular term in an arithmetic sequence.
- 206e: Determine the term in an arithmetic sequence closest to a particular number.
- 205: Exam Practice: nth term formula for arithmetic sequences (no standard formulae)
- 206: Exam Practice: Determining if a term belongs in an arithmetic sequence
Further Practice
- Practise Questions
EXTENSION MATERIALS
2.3 Arithmetic Sequences: nth Term Formula
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
How To Find The Nth Term of an Arithmetic Sequence by The Organic Chemistry Tutor
Online Platforms (with Videos & Exercises)
Activities
- Pixi Maths
Worksheets
- Dr Austin Maths
- Arithmetic Sequences Practice Strips (Editable Word | PDF | Answers)
- Arithmetic Sequences Crack the Code (Editable Word | PDF | Answers)
Dr Frost resources
Dr Frost Video
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
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.
- 573d: Determine a term of an arithmetic sequence used to model a given context.
- 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)
Further Practice
- Practise Questions
EXTENSION MATERIALS
2.4 Arithmetic Series
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Proof of Sum of an Arithmetic Series by Corbettmaths
Arithmetic Series – Sum of the Terms of Arithmetic Sequence by Math Teacher Gon
A-Level Maths: D4-07 Arithmetic Sequences: Examples of Finding the Sum of Arithmetic Series by TLMaths
Online Platforms (with Videos & Exercises)
Activities
- Pixi Maths
Worksheets
- Dr Austin Maths
- Sum of an Arithmetic Series Fill in the Blanks (Editable Word | PDF | Answers)
- Sum of an Arithmetic Series Practice Strips (Editable Word | PDF | Answers)
- Harder Sum of a Series Fill in the Blanks (Editable Word | PDF | Answers)
- Arithmetic Sequences Revision Practice Grid (Editable Word | PDF | Answers)
- Pixi Maths
Dr Frost resources
Dr Frost Video
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
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.
- 574c: Find the sum of the first n terms of an arithmetic series used to model a given context.
- 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.
- 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.
- 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
- Practise Questions
EXTENSION MATERIALS
3.1 Geometric Sequences
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Geometric Progressions
Online Platforms (with Videos & Exercises)
Activities
Worksheets
Dr Frost resources
Dr Frost Video
K407: Determine the nth Term of a Geometric Sequence.
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
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
- 203g: Generate a geometric sequence given the first term and the common ratio.
- 203l: Determine the next term(s) in a geometric sequence.
- 203o: Determine a later term in a geometric sequence.
- 203s: Determine a missing term in a geometric sequence with a single gap.
- 203v: Continue a geometric sequence where terms are algebraic.
- 370a: Determine the nth term for a geometric sequence of the form an for positive integers a.
- 370b: Determine the nth term for a geometric sequence of the form kan for positive integers a.
- 370c: Determine the nth term for a geometric sequence of the form kan where all terms are negative.
- 370d: Determine the nth term for a geometric sequence of the form kan for negative integers a.
- 370e: Determine the nth term for a geometric sequence of the form kan for decimal or fractional a.
- 370f: Determine the nth term for a geometric sequence of the form kan where a is a surd.
- 370g: Determine the common ratio of a geometric sequence where the terms are expressed algebraically.
- 203: Exam Practice: Describing, generating and continuing sequences using term-to-term rules
- 370: Exam Practice: nth term formula for a geometric sequence (no standard formulae)
Further Practice
- Practise Questions
EXTENSION MATERIALS
4.1 Other Famous & Recognisable Sequences
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Fibonacci Sequences
Online Platforms (with Videos & Exercises)
Activities
- Pixi Maths
Worksheets
- Dr Austin Maths
- Fibonacci Sequences Practice Strips (Editable Word | PDF | Answers)
- Corbettmaths
- Maths 4 Everyone
- Pixi Maths
Dr Frost resources
Dr Frost Video
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
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
- 202a: Identify named sequences such as square numbers, cube numbers, triangular numbers and the Fibonacci sequence.
- 202b: Identify if a sequence is arithmetic, quadratic or geometric.
- 203k: Determine the next term(s) in a sequence of triangular numbers.
- 203t: Continue a Fibonacci sequence.
- 203w: Continue a Fibonacci sequence where terms are algebraic.
- 202: Exam Practice: Distinguishing between different types of sequences
- 203: Exam Practice: Describing, generating and continuing sequences using term-to-term rules
Further Practice
- Practise Questions
EXTENSION MATERIALS
Activities
- Dr Austin Maths
- Josephus Problem Activity (Editable Word | PDF | Answers)
5.1 Quadratic Sequences: Recognising & Finding Next Terms
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Online Platforms (with Videos & Exercises)
Activities
- Maths 4 Everyone
- Pixi Maths
Worksheets
- Dr Austin Maths
- Generating Quadratic Sequences Practice Strips (Editable Word | PDF | Answers)
Dr Frost resources
Dr Frost Video
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
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
- 203f: Generate a quadratic sequence given the first two terms and the common second difference.
- 203j: Determine the next term(s) in a quadratic sequence.
- 203n: Determine a later term in a quadratic sequence.
- 203: Exam Practice: Describing, generating and continuing sequences using term-to-term rules
Further Practice
- Practise Questions
EXTENSION MATERIALS
5.2 Quadratic Sequences: Finding nth Terms
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Quadratic Sequences Version 1
Corbett Maths Quadratic Sequences Version 2
Corbett Maths Quadratic Sequences Version 3
Online Platforms (with Videos & Exercises)
Activities
- Pixi Maths
Worksheets
- Dr Austin Maths
- Nth Term of a Quadratic Sequence Fill In The Blanks (Editable Word | PDF | Answers)
- More Nth Term of a Quadratic Sequence Fill In The Blanks (Editable Word | PDF | Answers)
- Nth Term of a Quadratic Sequence Practice Strips (Editable Word | PDF | Answers)
- Corbettmaths
- Quadratic Sequences Practice Questions & Solutions
- Quadratic Sequences Worksheet & Solutions
- Quadratic Sequences AQA Level 2 Practice Questions & Solutions
- Pixi Maths
Dr Frost resources
Dr Frost Video
K406: Determine the nth Term Formula of a Quadratic Sequence.
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
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
- 369a: Determine the nth term formula of a quadratic sequence by comparison to n2
- 369b: Determine the nth term formula of a quadratic sequence in the form n2+c
- 369c: Determine the nth term formula of a quadratic sequence in the form n2 +bn for positive b
- 369d: Determine the nth term formula of a quadratic sequence in the form n2 +bn for negative b
- 369e: Determine the nth term formula of a quadratic sequence in the form n2+bn+c
- 369f: Determine the nth term formula of a quadratic sequence in the form an2+c
- 369g: Determine the nth term formula of a quadratic sequence in the form an2 +bn
- 369h: Determine the nth term formula of a quadratic sequence in the form an2+bn+c
- 369i: Determine the nth term formula of a quadratic sequence in the form an2+bn+c where a is negative
- 369j: Determine the coefficients of a quadratic nth term rule given information about the terms in the sequence.
- 369k: Determine the position of a term in a quadratic sequence.
- 369l: Use an existing formula for a quadratic sequence to determine the formula for a similar sequence.
- 371a: Determine the nth term formula of a sequence, where the numerator and denominator are arithmetic sequences to be found.
- 371b: Determine the nth term formula of a sequence, where at least one of the numerator or denominator is quadratic.
- 371c: Determine the nth term formula of a sequence where at least one of the numerator or denominator is geometric.
- 371d: Determine the nth term formula for a cubic sequence.
- 369: Exam Practice: nth term formula for a quadratic sequence
- 371: Exam Practice: nth term formula for more complex sequences
Further Practice
- Practise Questions
EXTENSION MATERIALS
6.1 Limit of a Sequence (AQA Level 2)
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Dr Frost resources
EXTENSION MATERIALS
Whole Topic Summary Resources (Including Past Paper Questions)
Download Sequences PPQs as WW Powerpoint for Edexcel IGCSE, AQA GCSE, Edexcel GCSE or OCR GCSE (or all GCSE together)