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- Question 1 and 2 Exercise 4.1
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... Given: $$a_n=\dfrac{n(n+1)}{2}$$ For first term, put $n=1,$ $$a_1=\dfrac{1(1+1)}{2}=1$$ For second term, put $n=2$. $$a_2=\dfrac{2(2+1)}{2}=3$$ For third term, put $n=3,$ $$a_3=\dfrac{3(3+1)}{2}=6$$ For forth ter
- Question 4 Exercise 4.5
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... 8}{1-0.1}=\dfrac{0.8}{0.9}=\dfrac{8}{9}$$\\ Hence putting $S_{\infty}$ in (i), we get $$0 . \overline{... ots \ldots \ldots . . . \text { (ii) }\end{align} Putting (ii) in (i), we get\\ $$1.63=1+\dfrac{7}{11}... s and given by $$S_{\infty}=\dfrac{a_1}{1-r}$$,\\ putting $a_1, r$ we get\\ $$S_{\infty}=\dfrac{0.15}{
- Question 2 & 3 Exercise 4.4
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... htarrow r^2&=9 \text { or } r= \pm 3 .\end{align} Putting this in (i), then\\ $$a_1(9)=27 \quad \text... \ \Rightarrow r&=-\dfrac{1}{\sqrt{2}}.\end{align} Putting in (i), then\\ \begin{align}\Rightarrow a_1(... that\\ \begin{align}a_n&=a_1 r^{n-1}, \\ \text { putting } n&=7, \text { and } a_1, r \text { then we
- Question 13 & 14 Exercise 4.5
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... ts and is given by $S_{\infty}=\dfrac{a_1}{1-r}$, putting $a_1, \quad r$, we get $$S_{\infty}=\dfrac{1}{1-\dfrac{x}{3}}=\dfrac{3}{3-x}$$ putting in (i), we have \begin{align}1+y&=\dfrac{3}{... htarrow S_7&=10,0.9921875\\ &=9.921875\end{align} Putting (ii) in (i), we get\\ \begin{align}S&=10+2(9
- Question 10 Exercise 4.4
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... t{a b}=36 \text {. }$$ From (i), we have $a=b+48$ pulting in (ii), then we have\\ \begin{align}(b+48+b... \Rightarrow 36 b&=36 \text { or } b=1\end{align} Putting $b=1$ in (i), we get\\ \begin{align}a-1&=48\
- Question 5 & 6 Exercise 4.5
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... d \text{and}\quad S_5=\dfrac{a_1(r^5-1)}{r-1}$$\\ Putting both the $S_{10}$ and $S_S$ in the given equ... =\dfrac{a_1(r^{3 n}-1)}{r-1}...(iii)\end{align}\\ Puting (i),(ii) and (iii) in L.H.S of the given, we
- Question 15 & 16 Exercise 4.5
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... 0 days is $$S_{30}=\dfrac{a_1(r^{30}-1)}{r-1} $$ putting $r-2$ and $a_1=1$, then \begin{align}S_{30}... g geometrically, we know that $a_n=a_1 r^{n-1}$, putting $a_1$ and $n=7$, then \begin{align}&729000=6
- Question 3 and 4 Exercise 4.2
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... ence has same distance $2$, hence it is an A.P. Putting $n=7$ in (1), we get $$a_7=2(7)+7=14+7=21.$$
- Question 17 Exercise 4.2
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... \implies &-10d=-30 \\ \implies &d=3.\end{align} Putting value of $d$ in (i), we get \begin{align}&n=
- Question 5 & 6 Exercise 4.3
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... ightarrow-5 d&=5 \\ \Rightarrow d&=-1.\end{align} Putting $d=-1$ in (i), we have\\ \begin{align}3 x_1+
- Question 7 & 8 Exercise 4.3
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... dfrac{n(6 n+4)}{2}=n(3 n+2) \text {. }\end{align} Putting (i),(ii) and (iii) in (1), we get\\ \begin{a
- Question 13 & 14 Exercise 4.3
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... \begin{align}S_n&=\dfrac{n}{2}[a_1+a_n],\\ \text{ putting the given}\\ 459&=\dfrac{n}{2}[1+50] \\ \Rig
- Question 3 Exercise 4.5
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... \Rightarrow r&=\dfrac{1}{2} \text {, }\end{align} putting this in (i), we have\\ \begin{align}\dfrac{a
- Question 7 & 8 Exercise 4.5
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... rrow a^3&=1728\\ \Rightarrow \quad a&=12,\\ \text{putting}\text{in} (1)\\ \dfrac{12}{r}+12+12 r&=38\\
- Question 9 & 10 Exercise 4.5
- unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... e know that:\\ $$S_n=\dfrac{a_1(r^n-1)}{r-1},$$\\ putting the given\\ \begin{align}40+13 \sqrt{3}&=\df