What is an arithmetic sequence?

An arithmetic sequence is a list of numbers where the difference between consecutive terms is always the same. For example, 5, 9, 13, 17 has a common difference of 4. The nth term formula is: a + (n-1)d, where a is the first term and d is the common difference.

How do you find the nth term of a sequence?

For an arithmetic sequence, find the common difference (d). Then the nth term = d x n + (first term - d). For example, the sequence 3, 7, 11, 15 has d = 4 and first term 3. So nth term = 4n + (3-4) = 4n - 1. Verify: when n=1, 4(1)-1 = 3. Correct.

What are triangular numbers?

Triangular numbers are formed by adding consecutive natural numbers: 1, 1+2=3, 1+2+3=6, 1+2+3+4=10, and so on. They are called triangular because that many dots can be arranged in a triangle. The nth triangular number equals n(n+1)/2.

Worksheets

Patterns & Sequences Class 6 IB Worksheet Free PDF Download with Answers

Find the rule, predict the future. 60 questions on number patterns, visual sequences, nth term rules, and pattern generalisation.

IBClass 6

SparkEd Team · Reviewed by Vivek Verma15 April 20267 min read

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45 practice questions across 3 difficulty levels with complete answer keys. Printable A4 format, perfect for revision!

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Class 6 Maths Worksheet — Free PDF with Answers

This is your one-stop class 6 maths worksheet collection — every topic, every chapter, completely free with step-by-step answers. Whether you searched for a maths class 6 worksheet or a worksheet math class 6 resource, you have landed in the right place. SparkEd's Class 6 maths practice covers the full IB MYP syllabus with 60 questions per topic, and each worksheet comes as a printable PDF.

Parents and teachers often look for a class 6 maths chapter 7 worksheet with answers or a class 6 maths chapter 3 worksheet with answers — here you will find those and every other chapter too. Every class 6th maths worksheet is aligned to the latest IB MYP pattern, so the maths worksheets of class 6 you download match exactly what is taught in school. Need a quick class 6th mathematics solution or a handy class 6th math formula sheet? Check out the Class 6 All Formulas guide.

Each maths worksheet for class 6 includes a mix of short-answer, long-answer, and maths questions and answers for class 6 in MCQ format. You get a complete maths worksheet for class 6 with answers, making self-study easy. The content is suitable as a maths worksheet for class 6 cbse as well as a maths worksheet for class 6 ncert resource — both boards follow the same core syllabus. Looking for a simpler label? It is the same math worksheet for class 6 you need.

For revision before exams, try the maths worksheet for class 6th with answers alongside our maths mcq for class 6 with answers sets. Teachers can use the class 6 maths mcq question paper bank for quick classroom tests. Browse all class 6 maths worksheets cbse topics on the All Class 6 worksheets page, or start with the popular Number Play worksheet. Ready to practise? Head to SparkEd home and pick your chapter.

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IB MYP Maths Worksheet — Free PDF with Answers

SparkEd's IB MYP Year 1 maths worksheets are designed for students in the International Baccalaureate Middle Years Programme. Each worksheet has 60 questions across three difficulty levels, with complete step-by-step answers.

Whether you are exploring sequences for the first time or preparing for a criterion assessment, these worksheets are free to download as printable PDFs.

Want to practise Patterns and Sequences digitally? Try free online practice on SparkEd — instant grading, visual solutions, and an AI coach to help when you are stuck.

Patterns and Sequences — Mathematics as a Detective Story

The IB MYP framework considers patterns to be at the very core of mathematics. Finding patterns is how mathematicians discover new theorems, and it is how scientists predict what happens next.

In this chapter, you learn to spot patterns in numbers and shapes, describe them using rules, and use those rules to predict terms far into the sequence. The big idea is generalisation — moving from specific examples to a general rule.

This worksheet takes you from simple "what comes next" problems to writing algebraic nth-term rules for sequences.

What Does This Worksheet Cover?

Aligned with the IB MYP Year 1 mathematics framework:

- Number patterns — arithmetic sequences (constant difference)
- Visual/geometric patterns — growing shapes, dot patterns
- Finding the rule — describing a pattern in words
- nth term — writing an algebraic rule for the general term
- Predicting terms — using the rule to find the 50th or 100th term
- Special sequences — square numbers, triangular numbers, Fibonacci
- Pattern investigation — testing and justifying pattern rules

| Level | Focus | Count |
|-------|-------|-------|
| Level 1 | Continue patterns, describe rules in words, identify special sequences | 20 |
| Level 2 | Find the nth term for arithmetic sequences, visual pattern tables | 20 |
| Level 3 | Complex patterns, justify rules, predict large terms, non-linear patterns | 20 |

Sample Questions

Level 1 — Warm Up

Find the next three terms: $3, 7, 11, 15, \ldots$
What type of sequence is $1, 4, 9, 16, 25, \ldots$ ? What is the next term?
Describe the rule for the pattern: $5, 10, 15, 20, 25, \ldots$

Level 2 — Build Confidence

A pattern starts at $4$ and increases by $6$ each time. Write the nth term rule.
A dot pattern shows: Figure 1 has 3 dots, Figure 2 has 5 dots, Figure 3 has 7 dots. How many dots in Figure 10?
The Fibonacci sequence is $1, 1, 2, 3, 5, 8, \ldots$ Find the next 4 terms.

Level 3 — Push Yourself

The nth term of a sequence is $n^2 + 1$ . Find the first 5 terms and the 20th term.
A pattern of matchsticks: Figure 1 uses 4 matches (a square), Figure 2 uses 7 matches (2 squares sharing a side), Figure 3 uses 10 matches. Write the nth term and find how many matches are needed for Figure 50.
Triangular numbers are $1, 3, 6, 10, 15, \ldots$ The nth triangular number is $\frac{n(n+1)}{2}$ . Find the 12th triangular number.