Exercise 6.4 Class 11 Math Solutions - Unit 6 Sequences and Series, Punjab Board

Step-by-step solutions to Exercise 6.4, Unit 6: Sequences and Series, for Class 11 Punjab Board students. Covers summation formulas for Arithmetic Series Sₙ = n/2 [2a₁ + (n - 1)d] and Sₙ = n/2 [a₁ + aₙ], finding the number of terms given a sum, and solving real-world word problems worked out question by question.

This page provides complete, step-by-step solved solutions for Exercise 6.4 of Unit 6: Sequences and Series for Class 11 Mathematics under the Punjab Board (PCTB / PECTAA). All questions on evaluating the sum of n terms of an Arithmetic Series using Sₙ = n/2 [2a₁ + (n - 1)d] and Sₙ = n/2 [a₁ + aₙ], finding unknown term counts, extracting the general term via aₙ = Sₙ - Sₙ₋₁, and solving real-world word problems are thoroughly worked out for HSSC Part 1 board exam preparation.
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Exercise Overview

Exercise 6.4 in Unit 6 of Class 11 Mathematics transitions from individual terms of an Arithmetic Progression to the summation of an Arithmetic Series. An arithmetic series is the indicated sum of the terms of an arithmetic progression: Sₙ = a₁ + a₂ + a₃ + ... + aₙ. Students are introduced to the fundamental summation formulas derived by Carl Friedrich Gauss: Sₙ = (n/2)[2a₁ + (n - 1)d] when the common difference is known, and Sₙ = (n/2)[a₁ + aₙ] when the initial and terminal terms are given.

The exercise tackles a comprehensive spectrum of algebraic problems, including calculating partial sums for given index ranges, solving quadratic equations in n to find the required number of terms that yield a specific target sum, and finding the nth term from sum functions via aₙ = Sₙ - Sₙ₋₁. In addition, it features real-world applied word problems such as financial loan repayments, seating capacity expansion in auditoriums, and physical acceleration scenarios.

In Punjab Board HSSC Part 1 examinations, Exercise 6.4 is one of the highest-yield sources for Section C long questions and Section B short questions across Lahore, Rawalpindi, Gujranwala, Faisalabad, Multan, and Sargodha boards. Practicing these step-by-step solutions gives students mastery over arithmetic series calculations and ensures flawless presentation in board exams.

FAQs

Are these Exercise 6.4 solutions according to the Punjab Board syllabus?
Yes, these solutions strictly follow the official Punjab Curriculum and Textbook Board (PCTB / PECTAA) syllabus for Class 11 Mathematics, covering Arithmetic Series summations and applied problems for the 2026-2027 academic session.
Do these solutions cover every question in Exercise 6.4?
Yes, every textbook problem from Exercise 6.4 is completely solved with step-by-step algebraic working, including calculating sums of finite APs, determining number of terms for a given sum, and solving practical word problems.
What are the formulas for finding the sum of n terms of an Arithmetic Series?
The sum Sₙ of n terms of an Arithmetic Series can be computed using Sₙ = (n / 2) [2a₁ + (n - 1)d] or Sₙ = (n / 2) [a₁ + aₙ], where a₁ is the first term, aₙ is the last term, and d is the common difference.
How do you find the nth term if the sum formula Sₙ is given?
The nth term aₙ can be evaluated directly from the sum formula by using the relation aₙ = Sₙ - Sₙ₋₁.
Can students read these solutions online?
Yes, students can read all Exercise 6.4 solutions directly online through MaryamNotes.pk on any device without needing to download external files or install third-party apps.
Are these solutions useful for Punjab Board exams?
Yes, sum of arithmetic series word problems and proving summation algebraic identities are among the most frequently tested Section C long questions and Section B short questions for HSSC Part 1.
Are these solutions based on the latest PCTB / PECTAA syllabus?
Yes, they are fully aligned with the updated Student Learning Outcomes (SLO) mandated by the Punjab Curriculum and Textbook Board (PECTAA) for the 2026-2027 academic year.
Are these solutions free for students?
Yes, all Class 11 Mathematics Exercise 6.4 solutions on MaryamNotes.pk are available entirely free of cost for students and teachers across Punjab.