====== Chapter 06: Sequences and Series ======
{{ :fsc:fsc_part_1_solutions:fsc-1-chap-06-ptb.jpg?nolink|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.
====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)//
====Solutions====
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  * Exercise 6.1  | [[vfsc1>ch06:view&cp=01&p=03&ch=06&fp=Ex-6-1-FSC-part1-ver3|View Online]]     | [[pdf>files/fsc/fsc_part1/ch06/dn.php?file=Ex-6-1-FSC-part1-ver3.pdf|Download PDF]] (115KB)

  * Exercise 6.2  | [[vfsc1>ch06:view&cp=01&p=04&ch=06&fp=Ex-6-2-FSC-part1-ver2|View Online]]     | [[pdf>files/fsc/fsc_part1/ch06/dn.php?file=Ex-6-2-FSC-part1-ver2.pdf|Download PDF]] (409KB)

  * Exercise 6.3  | [[vfsc1>ch06:view&cp=01&p=03&ch=06&fp=Ex-6-3-FSC-part1-ver3.1|View Online]]     | [[pdf>files/fsc/fsc_part1/ch06/dn.php?file=Ex-6-3-FSC-part1-ver3.1.pdf|Download PDF]] (123KB) UPD

  * Exercise 6.4  | [[vfsc1>ch06:view&cp=01&p=08&ch=06&fp=Ex-6-4-FSC-part1-ver2|View Online]]     | [[pdf>files/fsc/fsc_part1/ch06/dn.php?file=Ex-6-4-FSC-part1-ver2.pdf|Download PDF]] (757KB)

  * Exercise 6.5  | [[vfsc1>ch06:view&cp=01&p=04&ch=06&fp=Ex-6-5-FSC-part1-ver3|View Online]]     | [[pdf>files/fsc/fsc_part1/ch06/dn.php?file=Ex-6-5-FSC-part1-ver3.pdf|Download PDF]] (124KB)

  * Exercise 6.6  | [[vfsc1>ch06:view&cp=01&p=04&ch=06&fp=Ex-6-6-FSC-part1-ver2|View Online]]     | [[pdf>files/fsc/fsc_part1/ch06/dn.php?file=Ex-6-6-FSC-part1-ver2.pdf|Download PDF]] (332KB)

  * Exercise 6.7  | [[vfsc1>ch06:view&cp=01&p=02&ch=06&fp=Ex-6-7-FSC-part1-ver2|View Online]]     | [[pdf>files/fsc/fsc_part1/ch06/dn.php?file=Ex-6-7-FSC-part1-ver2.pdf|Download PDF]] (220KB)

  * Exercise 6.8  | [[vfsc1>ch06:view&cp=01&p=04&ch=06&fp=Ex-6-8-FSC-part1-ver2|View Online]]     | [[pdf>files/fsc/fsc_part1/ch06/dn.php?file=Ex-6-8-FSC-part1-ver2.pdf|Download PDF]] (389KB)

  * Exercise 6.9  | [[vfsc1>ch06:view&cp=01&p=02&ch=06&fp=Ex-6-9-FSC-part1-ver3|View Online]]     | [[pdf>files/fsc/fsc_part1/ch06/dn.php?file=Ex-6-9-FSC-part1-ver3.pdf|Download PDF]] (115KB)

  * Exercise 6.10 by Momin Ali |[[vfsc1>ch06:view&cp=01&p=09&ch=06&fp=Ex-6-10-FSC-part1-hw|View Online]] | [[pdf>files/fsc/fsc_part1/ch06/dn.php?file=Ex-6-10-FSC-part1-hw.pdf|Download PDF]] (560KB)
  
  * Exercise 6.10 |[[vfsc1>ch06:view&cp=01&p=04&ch=06&fp=Ex-6-10-FSC-part1-ver2|View Online]] | [[pdf>files/fsc/fsc_part1/ch06/dn.php?file=Ex-6-10-FSC-part1-ver2.pdf|Download PDF]] (365KB)

  * Exercise 6.11 | [[vfsc1>ch06:view&cp=01&p=07&ch=06&fp=Ex-6-11-FSC-part1-ver3|View Online]]     | [[pdf>files/fsc/fsc_part1/ch06/dn.php?file=Ex-6-11-FSC-part1-ver3.pdf|Download PDF]] (162KB)
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====Question Bank by Prof. Nusni Natasha====
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  * Chapter 06 (Question Bank)   | [[mdoku>fsc:fsc_part_1_solutions:ch06:viewer&cp=1&p=5&ch=06&fp=Ch06_Q_Bank|View Online]]     | [[pdf>files/fsc/fsc_part1/ch06/dn.php?file=Ch06_Q_Bank.pdf|Download PDF]] (410KB)
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====Short Questions====
The following short questions was send by Mr. [[people:akhtar]].
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  * Chapter 06 | [[aafsc1>short-question-ch06-fsc-part1-akhtar-abbas|View Online]] | {{:fsc:fsc_part_1_mcqs:short-question-ch06-fsc-part1-akhtar-abbas.pdf|Download PDF}} NEW
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