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WorksheetYear 11Level 3 · Challenge

Free Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3

Find the common difference or ratio, the nth term and the sum of arithmetic and geometric sequences. A challenge set for students ready to stretch further. This Year 11 worksheet has 10 questions and comes with a full answer sheet showing the working for every question.

Need more practice? Practice Set 2 · Practice Set 3 · Practice Set 4 — same skill, fresh questions, full answers.

Instant download · No sign-up · Free for personal, classroom and homeschool use

Year
Year 11
Subject
Maths
Topic
Sequences & Series
Difficulty
Level 3 · Challenge
Estimated time
20 minutes
Curriculum
New Zealand Curriculum
Questions
10
Answers
Included, with working
Format
PDF (A4), print or complete online

Students will practise

  • identifying arithmetic and geometric sequences
  • finding the nth term
  • summing arithmetic and geometric series

Curriculum: New Zealand Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.

What's next?

Completed: Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3

Ready for more? Move on to Year 12 Maths.

← Easier: Level 2 · StandardStudy guide

How to use this worksheet

  1. Print the PDF or complete it on screen. Write the student's name and date at the top.
  2. Read the instructions for each part together before starting. Encourage working to be shown, not just answers.
  3. Mark with the answer sheet. Compare the method, not only the final answer, and give credit for correct working.
  4. Record the score, celebrate what went well, then follow the "What's next" suggestion.

Common questions

Who is this worksheet for?

Year 11 students (typically ages 15–16) working on sequences & series. It is pitched at level 3 · challenge; an easier version is linked above.

Are the answers included?

Yes. The PDF includes a full answer sheet with the working for every question. You can also view the answers online.

How long does it take?

About 20 minutes for 10 questions. Short, regular sessions work best: two or three a week beats one long one.

Do I need to sign up to download?

No. Click Download Free PDF and it opens immediately. It is free for personal, classroom and homeschool use.

What should we do next?

Explore more Year 11 mathematics resources.

Preview

Success TutoringWorksheetsYear 11 · Mathematics · Sequences & Series

Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3

Name

Date

Score /

Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.

1.Find the 9th term of the arithmetic sequence −1, −5, −9, −13, …
2.Find the sum of the first 5 terms of the geometric sequence 8, 24, 72, 216, …
3.Find the sum of the first 29 terms of the arithmetic sequence 12, 16, 20, 24, …
4.Find the 6th term of the geometric sequence 7, 14, 28, 56, …
5.Find the sum of the first 8 terms of the geometric sequence −1, −5, −25, −125, …
6.For the geometric sequence 5, 15, 45, 135, …, write the common ratio and the rule for the nth term. (answer space)
7.Find the 26th term of the arithmetic sequence 5, 6, 7, 8, …
8.Find the sum of the first 12 terms of the arithmetic sequence 5, 10, 15, 20, …
9.For the geometric sequence 3, 12, 48, 192, …, write the common ratio and the rule for the nth term. (answer space)
10.Find the sum of the first 5 terms of the geometric sequence 2, 10, 50, 250, …
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Preview — the PDF contains the full resource and answer sheet.

More Year 11 sequences & series resources

  • Worksheet

    Year 11 Arithmetic and Geometric Sequences Worksheet — Level 1

    Find the common difference or ratio, the nth term and the sum of arithmetic and geometric sequences. Builds confidence with the core skill…

    Difficulty
    Level 1 · Easier
    Time
    20 min
    Questions
    10 questions
    Answers
    Answers included
  • Worksheet

    Year 11 Arithmetic and Geometric Sequences Worksheet — Level 2

    Find the common difference or ratio, the nth term and the sum of arithmetic and geometric sequences. Expected-level practice for this year…

    Difficulty
    Level 2 · Standard
    Time
    20 min
    Questions
    10 questions
    Answers
    Answers included

Sequences & Series in other year levels

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About this resource

Created by
Success Tutoring Maths Team
Reviewed by
Success Tutoring
Last reviewed
1 October 2026
How it was made
Generated by checked procedures

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