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Chapter 06: Sequences and Series

Notes (Solutions) of Chapter 06: Sequences and Series, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.

Geometric series

Contents & summary

  • Introduction
  • Types of Sequences
    • Exercise 6.1
  • Arithmetic Progression(A.P)
    • Exercise 6.2
  • Aritmetic Mean (A.M)
    • n Arithmetic Means between two given Numbers
    • Exercise 6.3
  • Series
    • Exercise 6.4
  • World Problems on A.P.
    • Exercise 6.5
  • Geometric Progression(G.P)
    • Exercise 6.6
  • Geometric Means
    • n Geometric Means between two given numbers
    • Exercise 6.7
  • Sum of n terms of a Geometric Series
  • The Infinite Geometric Series
    • Exercise 6.8
  • World Problems on G.P.
    • Exercise 6.9
  • Harmonic Progression(H.P)
    • Harmonic Means
    • n Harmonic Means between two numbers
  • Relation between Arithmic, Geometric and Harmonic Means
    • Exercise 6.10
  • Sigma Notation(or Summation Notation)
  • To find the Formulae of Sum
    • Exercise 6.11

Some corrected solutions

Exercise 6.2⇒ Question 11(i)

If $l,m,n$ are the $p$th, $q$th, $r$th terms of an A.P., show that $$l(q-r)+m(r-p)+n(p-q)=0$$ Solution: Let $a_1$ be first term and $d$ be common difference of A.P, then $$\begin{align}l=a_1+(p-1)d,\\ m=a_1+(q-1)d,\\ n=a_1+(r-1)d.\end{align}$$ Now $$\begin{align}L.H.S &= l(q-r)+m(r-p)+n(p-q)\\ &= lq-lr+mr-mp+np-nq\\ &=(l-n)q+(m-l)r+(n-m)p\\ &=(a_1+(p-1)d-a_1-(r-1)d)q+( a_1+(q-1)d-a_1-(p-1)d)r\\ &\,\,+(a_1+(r-1)d-a_1-(q-1)d)p\\ &=((p-1)d-(r-1)d)q+( (q-1)d-(p-1)d)r+((r-1)d-(q-1)d)p\\ &=(p-1-r+1)dq+(q-1-p+1)dr+(r-1-q+1)dp\\ &=(p-r)dq+(q-p)dr+(r-q)dp\\ &=[pq-qr+qr-pr+pr-pq]d=(0)d=0=R.H.S\end{align}$$

Exercise 6.4⇒ Question 3(ii)

An equation $3n^2-17n-288=0$ should be $3n^2-17n-228=0$. … suggested by Abdullah Zafar (Garrison Academy Kharian)

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Exercise 6.1 View Online Download PDF (53.2KB)
Exercise 6.2 (Handwritten) View Online Download PDF (185KB)
Exercise 6.3 (Handwritten) View Online Download PDF (67.7KB)
Exercise 6.4 (Handwritten) View Online Download PDF (354KB)
Exercise 6.5 (Handwritten) View Online Download PDF (58KB)
Exercise 6.6 (Handwritten) View Online Download PDF (209KB)
Exercise 6.7 (Handwritten) View Online Download PDF (118KB)
Exercise 6.8 (Handwritten) View Online Download PDF (236KB)
Exercise 6.9 View Online Download PDF (47KB)
Exercise 6.10 View Online Download PDF (299KB)
Exercise 6.11 View Online Download PDF (95.2KB)

Question Bank by Prof. Nusni Natasha

Chapter 06 (Question Bank) View Online Download PDF (410KB)


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