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- Question 5 & 6 Exercise 4.5
- _{2 n}&=\dfrac{a_1(r^{2 n}-1)}{r-1} \ldots . . . (ii)\\ \text { and } S_{3 n}&=\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 get \begin{align}S_n(S_{3 n}-S_{2 n})&=\dfrac{a_1(r^n-1)}{r-1}[\
- Question 1 and 2 Exercise 4.1
- quence whose last term is $50 $. =====Question 1(ii)===== Classify into finite and infinite sequences... n this sequence, we don't know. =====Question 1(iii)===== Classify into finite and infinite sequences... of the sequence are $1,3,6, 10$. =====Question 2(ii)==== Find first four terms of the sequence with t... the sequence are $4,-8,16,-32$. =====Question 2(iii)==== Find first four terms of the sequence with t
- Question 6 & 7 Exercise 4.4
- {\mathbf{A 5}}=n\end{align} Multiplying (i) and (iii), we get\\ \begin{align}a_{10} \cdot a_{16}&=\ln ... \quad \ln &=m^2 \because m=a_1 r^{12} \text { by (ii) }\end{align} Hence showed that $\ln =m^2$. ====... , \dfrac{1}{a_1 r^{n-1}}$,\\ General term of the (ii) sequence is:\\ \begin{align}a_n&=\dfrac{1}{a_1 r... endent of $n$, \\ which implies that sequence in (ii) is also geometric sequence with common ratio $\d
- Question 4 Exercise 4.5
- . \overline{8}=\dfrac{8}{9}$$.\\ =====Question 4(ii)===== Convert each decimal to common fraction $1 ... 7}{11} \ldots \ldots \ldots \ldots . . . \text { (ii) }\end{align} Putting (ii) in (i), we get\\ $$1.63=1+\dfrac{7}{11}=\dfrac{18}{11} \text {. }$$\\ =====Question 4(ii)===== Convert each decimal to common fraction $2
- Question 3 and 4 Exercise 4.1
- he sequence is $\dfrac{n}{n+1}$. =====Question 3(ii)==== Write down the nth term of the sequence as s... e sequence is $(-1)^{n+1} 2 n$. =====Question 3(iii)==== Write down the nth term of the sequence as s... irst five terms are $3,2,3,2,3$. =====Question 4(ii)===== Write down the first five terms of each seq
- Question 2 & 3 Exercise 4.4
- 1 r^2=27\\ a_5&=a_1 r^4=243.\end{align} Dividing (ii) by (i), we get\\ \begin{align}\dfrac{a_1 r^4}{a_... text{the third term is}=a_3&=a_1 r^2=-\sqrt{2}...(ii)\end{align} Dividing (ii) by (i), we get\\ \begin{align}\dfrac{a_1 r^2}{a_1 r}&=-\dfrac{\sqrt{2}}{2}=
- Question 5 Exercise 4.1
- j-3)&=-1+1+3+5+7+9 .\end{align} =====Question 5(ii)===== Write each of the following series in expan... k 2^k& =-1+2-4+8-16.\end{align} =====Question 5(iii)===== Write each of the following series in expan
- Question 6 Exercise 4.1
- s $1,5,10,10,5,1,0,0,0, \ldots$. =====Question 6(ii)===== Find the Pascal sequence for $n=6$ by using... 1,6,15,20,15,6,1,0,0,0,\ldots$. =====Question 6(iii)===== Find the Pascal sequence for $n=8$ by using
- Question 12 & 13 Exercise 4.2
- is A.M between 12 and 18. GOOD =====Question 13(ii)===== Find the arithmetic mean between $\dfrac{1}... =\dfrac{7}{24}\end{align} GOOD =====Question 13(iii)===== Find the arithmetic mean between $-6,-216$.
- Question 16 Exercise 4.2
- metic mean by 5 , we get\\ $$5 A=\dfrac{65}{2}---(ii)$$ From (i) and (ii), we get\\ \begin{align}A_1+A_2+A_3+A_4+A_5=5A.\end{align} Hence sum of five A.Ms
- Question 2 Exercise 4.3
- _{17}=50$ and $S_{17}=442$. GOOD =====Question 2(ii)===== Some of the components $a_1, a_n, n, d$ and... {21}=60$, $d=5$ and $n=21$. GOOD =====Question 2(iii)===== Some of the components $a_1, a_n, n, d$ and
- Question 5 & 6 Exercise 4.3
- w 3 x_1+20 d&=-11 \ldots \ldots \ldots \ldots . .(ii) \end{align} Subtracting (ii) from (i), we get\\ \begin{align}(3 x_1+15 d)-(3 x_1+20 d)&=-6-(-11) \\
- Question 7 & 8 Exercise 4.3
- )}{2}=n(3 n+2) \text {. }\end{align} Putting (i),(ii) and (iii) in (1), we get\\ \begin{align}S_{3 n}&=S_n+S_n^{\prime}-(S_n^{\prime \prime}) \\ \Rightarr
- Question 1 Exercise 4.4
- 5,15,45,135,405, \ldots\end{align} =====Question(ii)===== Write the first five terms of geometric ric... , \dfrac{1}{2}, \ldots\end{align} =====Question(iii)===== Write the first five terms of geometric ric
- Question 8 Exercise 4.4
- 94 \quad \text{or} \quad -2.94$$ =====Question 8(ii)===== Find the geometric mean of $-6$ and $-216$ ... =36 \quad \text{or} \quad -36$$ =====Question 8(iii)===== Find the geometric mean of $x+y$ and $x-y$