Master finding term-to-term rules and specific terms with this comprehensive, print-and-go maths worksheet. This resource features structured sections covering arithmetic and geometric sequence extensions, along with calculations for advanced specific terms up to the 60th term, complete with full step-by-step worked solutions for easy marking or independent revision.

Featuring a clear mathematical progression across multiple pages, this single-resource download is perfectly aligned with the UK Key Stage 3 (KS3) and GCSE Maths specifications.

What’s Included in This Resource?
• High-Utility Student Worksheet Pages: Clean, minimalist handouts focused entirely on maths fluency—ready to print and distribute immediately to your class.
• Comprehensive 2-Part Practice Set: Balanced coverage tracking across step rules and high-order term evaluations.
• Full, Step-by-Step Worked Solutions Key: Every single question is fully expanded showing the matching step-by-step calculations for massive target positions (such as the 5th, 6th, 9th, 16th, 28th, 38th, 50th, 52nd, and 60th terms)—ideal for quick teacher marking, student peer-assessment, or independent home study.

Scaffolding & Question Progression
This worksheet breaks down sequence operations into highly organized, progressive sections:
• Section 1: Term-to-Term Rules & Pattern Extension: Students examine 12 distinct linear and exponential patterns to calculate the next two terms and explicitly determine the operational rule (such as Add 3, Subtract 6, or Multiply by 4).
• Section 2: Finding Specific Higher-Order Terms: Pushes students beyond basic listing by challenging them to calculate massive target positions (such as the 28th, 38th, 50th, 52nd, and 60th terms) using linear sequence structures.

Why Teachers and Cover Staff Love This Resource:
• Ready to Use: Simply print and hand out! Perfect for busy term schedules, focused lessons, or unexpected cover days.
• Extensive Step-by-Step Solutions: Saves you hours of marking time and allows students to self-assess or fix errors independently.
• Versatile Classroom Utility: Ideal for core secondary maths instruction, targeted remediation, homework tasks, short assessments, or focused exam prep.

Target Audience, Exam Boards, & Specifications:
• Key Stages: Key Stage 3 and Key Stage 4 (GCSE Foundation and Higher Tiers).
• Exam Board Alignment: Fully suitable for AQA, Edexcel, OCR, and iGCSE specifications requiring absolute fluency in extending and evaluating linear sequences.
• Subject Areas: GCSE Mathematics, Secondary School Maths, and Core Maths.