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

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

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

11 August 2026

pdf, 73.46 KB
pdf, 73.46 KB

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.

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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

Arithmetic Sequences, nth Term & Sum Worksheet Bundle | GCSE 9-1

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. Master linear sequences and arithmetic series with this complete maths worksheet bundle! Perfectly optimized for KS3 and GCSE 9-1 maths revision (Foundation and Higher), this print-and-go pack covers finding the nth term, extending patterns, and series summation with full step-by-step worked solutions. ________________________________________ Looking for a rigorous, print-and-go resource to help your students master arithmetic progressions and linear sequences? This GCSE 9-1 Arithmetic Sequences, nth Term & Sum Worksheet Bundle contains highly structured practice sheets designed to build fluency and algebraic confidence. Moving from basic sequence extension to multi-step series summation formulas, this bundle is perfect for formal lessons, independent revision, homework packs, cover work, or intervention groups! Every page includes an uncrowded, student-friendly layout and comes paired with a complete, step-by-step worked solution key showing the exact algebraic workings to find the nth term and sum. ________________________________________ **What's Included in This Bundle?** • **Introduction to Sequences:** Practice extending patterns, finding the next terms, and identifying the term-to-term rule. • **Finding the nth Term:** Step-by-step worksheets helping students write explicit algebraic expressions for any linear sequence using the formula dn + (a - d). • **Calculating Specific Higher Terms:** Target practice for identifying massive terms (such as working out the 50th term) using the general rule. • **Sum of an Arithmetic Sequence:** Focused practice utilizing the series summation formula Sn to calculate the total sum of finite sequences, consecutive even/odd numbers, and specific multiples. • **Identifying Arithmetic Progressions:** Mixed review problems to test whether a pattern is a true arithmetic sequence or a non-linear rule. ________________________________________ **Perfect For:** • KS3 Maths: Building a strong foundational mastery of linear patterns and basic algebraic manipulation. • KS4 / GCSE 9-1 Prep: Targeted revision for both Foundation and Higher tier students aiming for maximum marks on algebra questions. • Cover Lessons & Homework: Structured, self-explanatory layout that requires zero preparation from you or a cover teacher. ________________________________________

£3.35
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

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