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The nth term of a sequence worksheet (with solutions)

The nth term of a sequence worksheet (with solutions)

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

25 July 2026

pdf, 78.33 KB
pdf, 78.33 KB

A worksheet on finding the nth term of a given linear sequence. Solutions are included.

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A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

Bundle

Nth Term Linear & Quadratic Sequences Worksheet Pack | Algebra 1 / GCSE

Master number patterns with this comprehensive, no-prep Nth Term Linear & Quadratic Sequences Worksheet Pack | Algebra 1 / GCSE! Aligned to Key Stage 3, Key Stage 4, and GCSE Maths objectives, this extensive, ready-to-print resource packet covers finding term-to-term rules, writing linear nth term expressions, and evaluating quadratic sequences. Complete with highly detailed, step-by-step worked solutions, it is the ultimate time-saving tool for main lessons, homework packets, cover work, or exam revision. ________________________________________ Are your secondary mathematics students struggling to find common differences, identify term-to-term rules, or write formulas for quadratic patterns? Simplify your maths lesson planning with this high-utility Arithmetic and Quadratic Sequences Pack. This bundle contains carefully structured student worksheets designed to build computational confidence and algebraic fluency across critical sequence concepts. Every single student problem page comes paired with a highly detailed, full-solution worked answer key that maps out the exact common differences, second differences, and algebraic adjustments required to find the correct rule. It is perfect for student self-assessment, small group interventions, homework packets, cover lessons, or fast and easy teacher marking! **What's Inside this Worksheet Pack?** • **Core Rules & Generation:** Practice writing out the first terms of a sequence from given linear and quadratic formulas, and find specific high-index terms like the 10th term. • **Term-to-Term Rules:** Targeted problem sets focused on identifying the specific operation between consecutive terms and finding the next steps for positive, negative, and alternating patterns. • **Linear Nth Term:** Practice writing explicit expressions for standard arithmetic sequences and calculating high-value positions like the 50th or 100th terms. • **Quadratic Nth Term:** Scaffolded practice utilizing differences of differences (second differences) to determine precise algebraic formulas for quadratic patterns. • **Teacher Answer Keys:** Complete, step-by-step visual worked solutions matching every student worksheet layout page exactly. **Why Teachers Love This Pack:** • **Zero Prep Required:** Just print out the PDF pages and you are ready to go! • **Scaffolded Progressions:** Skills move logically from basic basic sequence rules to complex multi-step quadratic transformations. • **Clean Layouts:** Generous workspace for students to neatly keep track of their numbers, index changes, and algebraic working out. • **Detailed Worked Keys:** Perfect for leaving with cover teachers or distributing digitally via a virtual learning environment (VLE) for independent revision. **Curriculum Alignment:** • **UK National Curriculum** (GCSE Maths Higher & Foundation): o Objective A24: Recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci-type sequences, quadratic sequences, and simple geometric progressions. o Objective A25: Deduce expressions to find the nth term of linear and quadratic sequences. • **International Frameworks:** Excellent for Year 8, Year 9, Year 10, and Year 11 mathematics classes, as well as Higher Level IGCSE revision. ________________________________________

£3.90
Bundle

Sequences worksheets (with solutions)

3 Worksheets on the following: determining the next terms of a given sequence and the term-to-term rule, writing terms of a sequence given the nth term formula and finding the nth term formula given the first few terms of a sequence.

£2.80
Bundle

8th Grade nth Term of Arithmetic Sequences Worksheets | Math Answer Key

Three worksheets on generating a sequence given its nth term and finding the nth term given the first few terms of a sequence. Detailed solutions are provided. Mastering sequence formulas requires solid structural practice. Pupils need to confidently find patterns, generate linear expressions, and calculate distant terms. This comprehensive, multi-page worksheet pack provides a rigorous, step-by-step mathematical progression. Designed with a clean, spacious layout, these practice sheets eliminate visual clutter to keep your Key Stage 3 or Key Stage 4 pupils focused entirely on procedural fluency. Perfect for independent classroom tasks, maths mastery blocks, homework packs, cover lesson plans, or GCSE exam revision. **What's Included in This Resource Pack?** * **Worksheet 1: Finding Next Terms, Expressions, and Deep Terms** – Features structured sequence problems where pupils write the next two terms, construct the explicit nth term formula, and calculate a deep term (such as the 50th term). * **Worksheet 2: Finding the nth Term Formula** – Contains targeted practice problems exclusively focusing on finding a linear expression for the nth term from given numerical progressions. It covers both increasing and decreasing sequences with negative common differences. * **Worksheet 3: Generating Sequences from Rules** – Includes unique problems that reverse the process. Pupils are given explicit nth term rules (including positive, negative, and decreasing linear constants) and must generate the first four terms of the sequence. * **Complete Step-by-Step Answer Keys** – Full-page printed solution guides are included for every single problem section. The keys clearly show intermediate step details—such as extracting the first term, finding the common term-to-term difference, and applying the formula—enabling lightning-fast teacher marking or easy student self-assessment. **Curriculum Coverage & Educational Standards** This resource is fully mapped to ensure deep mastery of the UK National Curriculum (Key Stage 3 & 4) and international GCSE equivalents focusing on "Algebra - Sequences": * **KS3 Maths (National Curriculum):** Generate terms of a sequence from either a term-to-term or a position-to-term rule. Recognise arithmetic progressions and find the nth term of a linear sequence. * **KS4 / GCSE Maths (National Curriculum):** Deduce expressions to calculate the nth term of linear sequences. * **Australian Curriculum (ACARA):** AC9M8A01 - Create and continue numerical sequences involving rational numbers, describe the rule used to create the sequence and find missing terms. **Ideal Classroom Use Cases** * **Daily Arithmetic Starters:** Use a small selection of questions daily as a sequences warm-up. * **Independent Fluency Work:** Assign sheets during algebra lessons to assess calculation accuracy. * **Homework Packs:** Easy-to-print homework sheets that parents can easily follow. * **Supply Teacher Resources:** Fully self-explanatory layouts with solutions included for seamless cover lesson delivery. ________________________________________

£3.10
Bundle

GCSE 9-1 Sequences Bundle

A collection of 4 worksheets on arithmetic sequences based on the GCSE 9-1 specification. In these worksheets students are taught to understand and use common difference (d) and first term (a) in an arithmetic sequence, know and use nth term =a+(n-1)d and find the sum of the first n terms of an arithmetic series. Detailed solutions are included.

£3.35

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