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5. Sequences and series

#### FP1 Notes and Examples

You will receive a student booklet with gaps for the solutions to the examples to be filled in and a teacher’s booklet with detailed worked solutions.

#### C2 Notes and Examples

You will receive a student booklet with gaps for the solutions to the examples to be filled in and a teacher’s booklet with detailed worked solutions.

#### C1 Notes and Examples

You will receive a student booklet with gaps for the solutions to the examples to be filled in and a teacher’s booklet with detailed worked solutions.

#### Sequences-determining the rule and finding terms worksheet no 2 (with solutions)

A worksheet on determining the rule followed by arithmetic sequences and finding terms in specified positions.

#### Arithmetic Sequences

Lots of questions on finding the nth term of an arithmetic sequence (none of these questions refer to the summation). Answers are at the bottom of the sheet. Please let me know if you like it.

#### IB Maths HL - Complete Notes

Complete notes, without any option topics, just the main topics 1 to 6 This is a collection of all of the notes I have written for my IB Maths HL class. They are handwritten, concise notes, covering the whole course in 77 pages. Topic 1 - Algebra - 21 Pages Topic 2 - Functions - 10 Pages Topic 3 - Trigonometry - 6 Pages Topic 4 - Vectors - 10 Pages Topic 5 - Statistics &amp; Probability - 10 Pages Topic 6 - Calculus - 20 Pages If you would like to see what you would be getting, you can download Topic 1 of IB SL or IB Math Studies for free. I hope you enjoy, and please ‘follow’, as I will be uploading other IB resources soon.

#### Sequences-determining the rule and finding terms worksheet (with solutions)

A worksheet on determining the rule followed by arithmetic sequences and finding terms in specified positions.

#### The nth term of an arithmetic sequence worksheet (with solutions)

A worksheet on finding the nth term of an arithmetic sequence given its first terms. The formula dn+(a-d) is used. Solutions are included.

#### Edexcel New Linear Maths A Level Year 2 Topic 3: Sequences and series

These notes and examples are designed for the delivery of the new Edexcel A Level Maths Linear Specification. You will receive an editable Word document that can be issued to students with gaps for them to fill in the solutions to the examples and make further notes. Full solutions to the examples are provided for the teacher in the form of a PDF document. This could be made available to students if they miss a lesson, reducing teacher workload.

#### Edexcel Further Core Pure AS

These notes and examples contain everything you need to deliver the new Edexcel Further Core Pure AS content. There are 6 student booklets and 6 teacher booklets containing detailed solutions to all examples.

#### Edexcel Further Core Pure AS Topic 5: Proof by induction

These notes and examples are designed for the delivery of the new Edexcel A Level Further Maths Linear Specification. You will receive an editable Word document that can be issued to students with gaps for them to fill in the solutions to the examples and make further notes. Full solutions to the examples are provided for the teacher in the form of a PDF document. This could be made available to students if they miss a lesson, reducing teacher workload. Each topic is available as a separate purchase, or you can download the entire set covering all the the Core Pure AS content. To purchase the complete set of notes for the Core Pure AS content, click here: [https://www.tes.com/teaching-resource/edexcel-further-core-pure-as-11890483]

#### Edexcel Further Core Pure AS Topic 2: Further Algebra

These notes and examples are designed for the delivery of the new Edexcel A Level Further Maths Linear Specification. You will receive an editable Word document that can be issued to students with gaps for them to fill in the solutions to the examples and make further notes. Full solutions to the examples are provided for the teacher in the form of a PDF document. This could be made available to students if they miss a lesson, reducing teacher workload. Each topic is available as a separate purchase, or you can download the entire set covering all the the Core Pure AS content. To purchase the complete set of notes for the Core Pure AS content, click here: [https://www.tes.com/teaching-resource/edexcel-further-core-pure-as-11890483]

#### Introduction to Sequences Color by Number

With this activity, students will find terms of sequences and then color their answers on the picture according to the directions to reveal a beautiful, colorful mandala! As an added bonus, the final products make fabulous classroom decor! This activity is an excellent resource for sub plans, enrichment/reinforcement, early finishers, and extra practice with some fun. It is especially useful for end-of-year practice, spiral review, and motivated practice when students are exhausted from standardized testing or mentally “checked out” before a long break (hello summer!). Teachers and students alike enjoy motivating activities, so engage your students today with these fun coloring activities!

This can be used to generate quadratic and cubic sequences and uses difference table to show the step by step solution. It also has a quadratic solver which will give the nth term of a sequence. On the right hand side there are cells that can be copied and pasted to use the sequence.

#### C2 A Level Summary

“cheat sheet” covering all C2 topics for CCEA A Level. Use for revision classes/exercises as a guide or as a comfort blanket for a class test.

#### Algebra: Sequences / Series BIG BUNDLE (10 lessons) inc. loads of resources

This is a big bundle on sequences that includes everything needed for your GCSE classes and AS Level work on arithmetic and geometric series. 1. Introduction to Linear Sequences 2. Linear Sequences in Diagrams/Patterns 3. Quadratic Sequences 4. Cubic, Exponential and Other sequences 5. Fibonacci Sequence / Golden ratio and Spiral 6. Arithmetic Series 7. Sum of Arithmetic Series 8. Geometric Series 9. Sum of Geometric Series 10. Sum of infinite Series This is also available as a GCSE bundle only if that is your preference. NOTE: Feel free to browse my shop for more free and premium resources! As always please RATE and FEEDBACK (comments good or bad) thank you!

#### Advanced Higher Maths - Sequences etc. homework

A mixed homework with questions on arithmetic and geometric sequences, as well as practice complex numbers, binomial theorem and Gaussian elimination. Full solutions included

#### Sequences: Limits

Exercises to introduce limits of sequences, particularly for recurrence relations. The recurrence relation 2 exercise has in context application. All answers given. Exercises also on Promethean flipchart. Click on Design Mode to reveal all answers or edit. In recurrence relation 2 exercise, can click around the first line of the question to reveal/hide answer.

2 A4 sides with questions on quadratic sequences (or could be used as a test). Questions include next numbers in sequences finding the nth term and finding a term in the sequence. Followed by 2 A4 sides with answers. Suitable for years 8-11 higher and middle ability sets. L/O: To find nth term formula of quadratic sequences and find the term given a number in the sequence.

#### Algebra: Sequences 10 - Sum of Infinite Series (A-Level) + lots of resources

This is the last of my lessons on sequences and looks at convergent series and how to find the sum if the sequence is infinite. This is a helpful lesson tieing nicely other previous lessons on sequences. It comes with a starter, learning objectives, excellent teaching slides with plenty of examples and embedded exam questions, questions with answers and a plenary. Normally I would teach this material in about 30-40 minutes and spend the rest of the lesson and into homework looking at past exam questions. I have attached past exams questions that I use with mark scheme and a shorter answer format for photocopying reasons. NOTE: Feel free to browse my shop for more free and premium resources! As always please RATE and FEEDBACK (comments good or bad) thank you!

#### Algebra: Reciprocal and Exponential Graphs (+ worksheet and resources)

This is a lesson on teaching about reciprocal and exponential graphs. This begins with what these graphs look like with key points or characteristics. It then looks at drawing them and then problems associated such as finding gradients and solutions to equations. 20 slides + resources. The additional resources are an excellent differentiated worksheet to practise drawing and a few additional problems. It also comes with blank axis so pupils don't have to spend long periods drawing unnecessarily and also a handout to look at all different graphs. NOTE: Feel free to browse my shop for more free and premium resources! As always please RATE and FEEDBACK (comments good or bad) thank you!

#### Algebra: Sequences 9 - Sum of Geometric series (A-Level) + worksheet

This lesson builds on the previous lesson that introduced geometric sequences and series. This lesson focuses on where the formula comes from and how to use the formula for finding the sum of geometric sequences. It comes with a differentiated worksheet with different types of questions. The lesson comes with a starter, learning objectives, keywords, excellent teaching slides and examples, questions with answers and a plenary. This is part of a bigger bundle or series, which can either be purchased with or without the additional A-Level lessons. NOTE: Feel free to browse my shop for more free and premium resources! As always please RATE and FEEDBACK (comments good or bad) thank you!

#### Algebra: Sequences 8 - Geometric Sequences or Series (A-Level) + worksheet

This lesson builds on the previous lessons but does introduce GEOMETRIC sequences and series. The lesson looks at what a geometric sequence is, finding the common ratio in various problem-solving forms, individual terms and other problems. The worksheet is differentiated with suggested different starting points to see the type of questions that can be asked. It is an excellent worksheet that has accompanying answers. The lesson comes with a starter, learning objectives, keywords, excellent teaching slides and examples, questions with answers and a plenary. This is part of a bigger bundle or series, which can either be purchased with or without the additional A-Level lessons. NOTE: Feel free to browse my shop for more free and premium resources! As always please RATE and FEEDBACK (comments good or bad) thank you!

#### Arithmetic Sequence and Series - A-level Mathematics, Pure maths

In this lesson, learners will be able to understand and work with arithmetic sequences and series, including the formulae for nth term and the sum to n terms; work with sequences including those given by a formula for the nth term and those generated by a simple relation of the form xn+1 = f(xn); increasing sequences; decreasing sequences; periodic sequences; understand and use sigma notation for sums of series; Use sequences and series in modelling Lesson can be used as whole class teaching by teachers and at home by learners. Lots of drag and drop activity with instant feedback. To access online choose the multiscreen.html file. To access offline choose the swf file. Contains 53 interactive pages

#### OCR AS Maths Core 2 2017 Exam solutions - full explanations split by question

Fully explained and written solutions to the OCR 2017 AS Mathematics Core 2 exam paper. The questions are split by each part so that you can easily navigate to the parts you and the students want to look at. If you find this useful there are many other free exam solutions on my youtube channel: MissPennyMaths

#### Key revision points for C2 Core A-Level Maths

A collection of key points to remember for C2 Core AS Maths. Prevents against silly mistakes and allows students to reach top marks! Possible mistakes collected from the questions and mark schemes from 20+ past papers. Relevant to C2 content: &gt; Proof &gt; Logarithms &gt; Integration &gt; Differenciation &amp; differenciation from first principles &gt; Sequences and series &gt; Sectors &gt; Trigonometry and graphs &gt; Trig identities &gt; Log and exponential graphs &gt; Translations &gt; Significant figures &gt; Trapezium area calculations Information divided into clear headings with very important points highlighted in yellow. Recommended for A-Level Maths students taking C2, especially relevant for OCR MEI exam board. An invaluable collection of points to have before an exam.

#### KS4/KS5 maths convergence investigation

This investigation (includes teacher notes and worksheets) is suited to very able KS4 groups and those in KS5 studying Maths. It covers the topics of convergence, subject of a formula and even can be expanded to iteration for more advanced learners. Pupils are given a starting value of a sequence, which they multiply by 3, add 10 to then and finally divide by 4 to generate the next term in the sequence. They then multiply this value by 3, add ten to it and divide by 4 to get the next term and so forth, generating the sequence in an iterative manner until the sequence converges. The goal of this investigation is to find a relationship between the initial starting value of the sequence and that which it converges to. This can be explained in a satisfying algebraic way using subject of the formula although pupils may offer other alternative explanations.

#### Erica's Errors - A Level (Year 2) Bundle

Erica is struggling with many aspects of the A level mathematics course and needs help from your students. What you have here is 17of her homeworks, each with mistakes in solutions which your students need to find, correct and explain where Erica has gone wrong. These are purely designed to generate discussion and to allow students to demonstrate their understanding, whilst also allowing them to show their own methods of silving problems. These are all based upon the new A level curriculum.

#### Sequences - Required Skills, Examples and Investigation

A series of four worksheets to give some background algebra, do plenty of examples finding a limit, then for advanced pupils go on to find a general formula for a linear sequence. If you follow this through you will be able to instantly work out the value of the 50th term of u_n+1 = 0.4 u_n +3 (for example). The four worksheets are: - Indices (practice on this) - Algebra (rearranging formula) - Sequences (standard questions on finding limits, and graphing the results) - Investigation (putting it all together to get a general formula) All provided with full solutions.

#### Can you crack the code? Further maths revision challenge - perfect for new spec problem solving

For these lessons, I have a wooden box which I fill full of goodies (fruits, sweets etc). I then have a large metal chain wrapped around the box with a colourful padlock on (all of which builds the tension...). The aim is for the students to work away in pairs to crack the code! If you don't want to purchase the box etc, the worksheet works perfectly well on it's own. Note: the solution for this worksheet is 6452. This worksheet is a real challenge for your KS5 students - perfect for the new A Level demands.

#### Can you crack the code? Demanding AS Level revision - perfect for new spec - problem solving!!!

For these lessons, I have a wooden box which I fill full of goodies (fruits, sweets etc). I then have a large metal chain wrapped around the box with a colourful padlock on (all of which builds the tension...). The aim is for the students to work away in pairs to crack the code! If you don't want to purchase the box etc, the worksheet works perfectly well on it's own. Note: the solution for this worksheet is 8224. This worksheet is a real challenge for your KS5 students - perfect for the new AS Level demands.

#### IB Maths HL - Topic 1 Algebra - Notes

Handwritten notes that I made for my HL students on Topic 1 of Algebra in the IB. It includes: 1.1 - Sequences &amp; Series 1.2 - Exponents and Logs 1.3 - Binomial Expansion &amp; Permutations/Combinations 1.4 - Proof by Induction 1.5 - Complex Numbers 1.6 - Complex (Polar Form) 1.7 - De Moivre's Theorem/Euler's Theorem 1.8 - Complex Conjugate Roots of Polynomials 1.9 - Solving Systems of Equations with 3 variables If you are an HL teacher (or student) and you found these helpful, please 'follow' me, then you will see as soon as I get around to uploading the remaining topics of the HL course (Feb/March/April 2018).

#### Erica's Errors On Sequences and Series

Erica is getting a bit lost on arithmetic and geometric sequences and series. Could you please help her sort out her homework? Her errors will need explaining so that they aren't made again. A task designed to encourage discussion.

#### Colouring by Annuities - Obama, solve for PV, FV, & Interest (30 sheet mosaic)

Highly Engaging!! Each worksheet represents a small section of the big picture! The end result will look spectacular hanging up in your classroom :) INVOLVED: Each worksheet has 3 questions each of: • Find future value • Find present value • Determine total interest earned • Determine total interest paid It's simple! 1. Calculate the answers. 2. Colour the squares. 3. Cut out your section. 4. Combine with the class! Students complete the problems to decode the colour key, then use it to colour their section of Obama mosaic. High school kids like colouring too! Their curiosity and desire to see the big picture come together will keep them working and helping each other! INCLUDED (.pdf and .docx files): -&gt;Complete class set of 30 worksheets, that combine to create the Obama mosaic. Sheets contain the answers scrambled so students can monitor their own understanding. -&gt;Complete answer keys all worksheets. -&gt; Colour solution and coordinate guide for the mosaic. -&gt;Each worksheet contains 12 problems. Ontario Curriculum: This is great for MAP4C, or MCR3U. All my &quot;Colouring by...&quot; math mosaics use the standard colours found in a Crayola 24 pack of coloured pencils. For best results, use the exact colour name match. Maybe a class set of pencil crayons would be a fun departmental purchase? :) I'd love to hear from you! Leave some feedback through Tes about how this went in your classroom, or email me at calfordmath@live.ca

#### Erica's Errors On Binomial Expansion

Erica is struggling with the binomial expansion; can you (and your class) help Erica correct the answers she has arrived at and explain to her what she has done incorrectly. This is designed to create discussion and help students become familiar with new style questions.

#### Series Worksheet

Worksheet on sums of series - lesson-in-a-sheet with starter question followed by key information, main questions and then extension.

#### Homeworks (Pure) - New AS Further Maths Syllabus

I have included 3 sections as a free sample which you be able to find towards the bottom of this page. Split into 15 sections 1. Complex Numbers 1 2. Complex Numbers 2 3. Conic Sections 4. Hyperbolic Functions 5. Maclaurin’s Series 6. Matrices 1 7. Matrices 2 8. Method of Differences 9. Polar Coordinates 10. Proof by Induction 11. Rational Functions 12. Roots of Polynomials 13. Summation Series 14. Vectors 15. Vol. of Rev. and Mean Value Each section has 4 documents 1. Homework 2. Full worked solutions for homework 3. Challenge Questions for gifted students 4. Full worked solutions for Challenge Questions • Includes both the PDF’s and word documents which are fully editable. • They are written for the AQA syllabus but can be adapted for other exam boards. • The homework’s are intentionally quite difficult and written in an exam style. • Each homework has ~50% of the answers provided, this is to allow students to check they’re getting the first few questions correct. You can remove this if you want. Note: As there is a lot of content here there may be a few typos, I’ll be sure to update any mistakes as soon as I’m aware of them. The questions and solutions should be close to 100% accurate though.

#### Homeworks (Pure) - New AS Further Maths Syllabus

These are 3 free sample sections from my Further Maths Homework collection. You should be able to find the full 15 sections at the bottom of the page.

#### NEW SPECIFICATION maths A Level Quick reference (notes for students)

This is an extremely useful resource to help prepare for teaching the new maths A Level. It can be used to help structure the teaching of all topics (pure, statistics and mechanics). With a site license, teachers can distribute the document freely to students within their school either electronically or in print. This document makes a great reference tool for students to use throughout the course. Approximately 76 pages.