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.