Introduction
The best Unit 6, Sequences and Series, solved notes for Class 11 Punjab Boards are now available, with 100 percent of exercises solved using easy, step by step solutions and the marking scheme, based on the new book from PECTAA, the Punjab Curriculum and Textbook Board.
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These notes are perfect for the 2027 exams and are built to help students score 90 plus marks.
Ideal for Students, Teachers, and Lecturers Across All Nine Punjab Boards
These notes are used at top registered institutions across all nine Punjab boards, including Aitchison College Lahore, Sadiq Public School Bahawalpur, Army Public Schools and Colleges, Beaconhouse, Forman Christian College Lahore, Government College University Faisalabad, Cadet College Hasan Abdal
Cadet College Petaro, Cadet College Okara, Cadet College Kohat, Cadet College Sargodha, Cadet College Jhang, Cadet College Pasrur, Cadet College Spinkai, Military College Jhelum, Garrison Cadet College Kohat, and many more.
What’s Inside Unit 6, From Patterns to Provable Sums
Unit 6 opens with a simple question: what makes a list of numbers a sequence, rather than just a random list? From there it builds up the full toolkit for arithmetic sequences and series, before moving into geometric and harmonic sequences.
Section 6.1, Sequence, defines a sequence as a function whose domain is the natural numbers, introduces finite and infinite sequences, and shows how to generate terms from a given nth term formula, or write an nth term formula from a given pattern.
Section 6.2 introduces the Arithmetic Progression, where each term is formed by adding a fixed common difference to the previous term, along with the formula for the nth term.
Section 6.3, Arithmetic Mean, covers how to find one or more arithmetic means inserted between two numbers, and the relationships that hold between them.
Section 6.4, Series, defines a series as the sum of the terms of a sequence, and derives the formula for the sum of the first n terms of an arithmetic series, Sā = (n/2)[2aā + (n ā 1)d], with worked examples covering everything from summing the first 100 positive integers to reconstructing a series from partial information.
Section 6.5, Geometric Progression, is introduced next, defining the common ratio and the rule for the nth term of a G.P., setting up the geometric sequence and series work that continues later in the unit.
Exercise 6.1, Finding Terms of a Sequence, Fully Solved
All questions in Exercise 6.1 are fully solved, covering finding terms from a given pattern and from a given nth term formula.
| Question | Sequence | Result |
|---|---|---|
| Q1(i) | 12, 16, 20, … | Next four terms: 24, 28, 32, 36 |
| Q1(ii) | 3, 1, ā1, … | Next four terms: ā3, ā5, ā7, ā9 |
| Q2(i) | aā = 3n + 5 | First three terms: 8, 11, 14 |
| Q2(ii) | aā = 3, aāāā = 4aā ā 7 | First three terms: 3, 5, 13 |
| Q2(iii) | aā = (n ā 3)(n + 1) | First three terms: ā4, ā3, 0 |
| Q2(iv) | aā = ā1, aāāā = 3/(aā + 2) | First three terms: ā1, 3, 3/5 |
| Q2(v) | aā = 8 ā 20/(3 + n) | First three terms: 3, 4, 14/3 |
| Q2(vi) | aā = 1, aāāā = (3aā + 2)Ā² | First three terms: 1, 25, 5929 |
| Q2(vii) | aā = (ā2n)Ā² | First three terms: 4, 16, 36 |
The full solved PDF for Exercise 6.1 is available, covering every question in complete detail, including the triangular number question later in the exercise.
Exercise 6.2, Arithmetic Sequences, Fully Solved
Exercise 6.2 is fully solved, covering finding the common difference and general terms of an arithmetic sequence, checking whether a number belongs to a given A.P., and word problems built around the arithmetic sequence formula.
Exercise 6.3, Arithmetic Means, Fully Solved
Exercise 6.3 is fully solved, covering finding one or more arithmetic means between two numbers, and proving relationships that arithmetic means satisfy.
Exercise 6.4, Arithmetic Series, Fully Solved
Exercise 6.4 is fully solved, covering summing arithmetic series directly, finding Sā from given values of aā, n, and d, and word problems that translate into arithmetic series, including a right-angled triangle problem and several series reconstruction questions.
Coming Soon, Geometric and Harmonic Progressions
Section 6.5, Geometric Progression, along with the geometric series, harmonic sequences, and any further sections and exercises in this unit, will be added to these notes shortly. (Note for the team: this document only carries verified content through Exercise 6.4; the remaining pages are needed before that material can be added here.)
Bonus Resources
- A Sequences and Series formula sheet PDF for quick reference.
- Shortcuts for arithmetic sequence and series problems.
- Sequences and Series video lectures.
- Unit 7 is coming soon as the next unit in this series.
View the Full Solved PDF
The complete solved PDF for Unit 6 is available to view for free, with no download needed.
Official Youtube Channel : www.youtube.com/@PECTAAlearnersclub
Why This Unit Matters for Your Overall Score
Sequences and Series is a unit that rewards pattern recognition just as much as formula memorization. Getting comfortable with the arithmetic sequence and series formulas in Sections 6.2 to 6.4 builds the foundation for the geometric and harmonic sequence work that follows, since all three sequence types share the same underlying logic of finding a rule that connects consecutive terms.
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Frequently Asked Questions
Which exercises are covered in these Unit 6 notes? Exercise 6.1 through Exercise 6.4 are covered in full, with complete step by step solutions, spanning sequences, arithmetic sequences, arithmetic means, and arithmetic series.
What’s the difference between a sequence and a series? A sequence is an ordered list of terms, while a series is the sum of those terms. If aā, aā, aā, … is a sequence, then aā + aā + aā + … is its corresponding series, as shown in Section 6.4.
Are past papers included with these notes? Yes, Unit 6 past papers solved from 2018 through 2025 are included as a bonus resource.
Do I need to download the PDF to view these notes? No, the full solved PDF can be viewed directly on the site for free, with no download required.
Conclusion
With Exercise 6.1 through Exercise 6.4 fully solved, Class 11 students across all nine Punjab boards have a strong start on Sequences and Series ahead of the 2026 exams, with the geometric and harmonic progression material to follow shortly. Use these notes alongside the bonus formula sheet, shortcuts, and past papers to build both speed and accuracy for your Mathematics exam.
Best of luck for your Class 11 Mathematics exam!