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- Question 3 & 4 Exercise 4.3
- rac{66}{2}(25+350) \\ \Rightarrow S_{66}&=33(375)=12375 .\end{align} =====Question 4===== The sum of ... a+d)&=36 \\ \Rightarrow 3 a&=36 \\ \Rightarrow a&=12\end{align} Now by the second condition, the sum o... \Rightarrow 3 a^3+6 a d^2&=6336 \\ \Rightarrow 3(12)^3+6(12) d^2&=6336 \text { as } a=12 \\ \Rightarrow 3(1728)+72 d^2&=6336 \\ \Rightarrow 72 d^2&=6336-
- Question 4 Exercise 4.5
- rt each decimal to common fraction $0 . \overline{123}$ ====Solution==== Since $$0 . \overline{123}=0.123+0.000123 +0.000000123+\ldots$$ \begin{align}\text{or}\quad 0 . \overline{123}&=0.123+(0.001)(0.123)
- Question 7 & 8 Exercise 4.5
- 28\\ \Rightarrow a^3&=1728\\ \Rightarrow \quad a&=12,\\ \text{putting}\text{in} (1)\\ \dfrac{12}{r}+12+12 r&=38\\ \Rightarrow \dfrac{1}{r}+1+r&=\dfrac{38}{12}=\dfrac{19}{6}\\ \Rightarrow \dfrac{r^2+r+1}{r
- Question 12 & 13 Exercise 4.2
- ====== Question 12 & 13 Exercise 4.2 ====== Solutions of Question 12 & 13 of Exercise 4.2 of Unit 04: Sequence and Serie... KPTB or KPTBB) Peshawar, Pakistan. =====Question 12===== A man earned dollars 3500 the first year he ... tion 13(i)===== Find the arithmetic mean between $12$ and $18$. GOOD ====Solution==== Here $a=12, b=18
- Question 5 & 6 Exercise 4.3
- hose sum is $20$ and the sum of whose squares is $120$ . ====Solution==== Let the four numbers are\\ $... lign} $Condition-2$\\ The sum of their square is $120$, therefore\\ \begin{align}(a-3 d)^2+(a-d)^2+(a+d)^2+(a+2 d)^2&=120 \\ \Rightarrow a^2-6 a d+9 d^2+a^2-2 a d+d^2+a^2+2 a d+d^2+a^2+6 a d+9 d^2&=120 \\ \Rightarrow 4 a^2+20 d^2&=120 \\ \Rightarrow
- Question 11 & 12 Exercise 4.3
- ====== Question 11 & 12 Exercise 4.3 ====== Solutions of Question 11 & 12 of Exercise 4.3 of Unit 04: Sequence and Series. Th... ix seconds is $576 \mathrm{ft}$.\\ =====Question 12===== Afzal Khan saves Rs. $1$ the first day, Rs.
- Question 6 & 7 Exercise 4.4
- \begin{align}a_{10}&=a_1 r^9=l \\ a_{13}&=a_1 r^{12}=m\\ \text{and} \quad a_{16}&=a_1 e^{\mathbf{A 5}... &=a_1^2 r^{24} \\ \Rightarrow \quad \ln &=(a_1 r^{12})^2 \\ \Rightarrow \quad \ln &=m^2 \because m=a_1 r^{12} \text { by (ii) }\end{align} Hence showed that $
- Question 12 Exercise 4.4
- ====== Question 12 Exercise 4.4 ====== Solutions of Question 12 of Exercise 4.4 of Unit 04: Sequence and Series. This is... KPTB or KPTBB) Peshawar, Pakistan. =====Question 12===== For what value of $n, . \dfrac{a^{n+1}+b^{n+
- Question 11 & 12 Exercise 4.5
- ====== Question 11 & 12 Exercise 4.5 ====== Solutions of Question 11 & 12 of Exercise 4.5 of Unit 04: Sequence and Series. Th... -r} b^{r-p} c^{p-q}&=1.\end{align} =====Question 12===== Find an infinite geometric series whose sum
- Question 14 Exercise 4.2
- ign}A_3&=a+3 d=6+3 \cdot \dfrac{35}{4}\\ &=\dfrac{129}{4}=32\dfrac{1}{4}.\end{align} Hence three arith... ry">[[math-11-kpk:sol:unit04:ex4-2-p9 |< Question 12 & 13 ]]</btn></text> <text align="right"><btn typ
- Question 16 Exercise 4.2
- c{13}{2}+7+\dfrac{15}{2}\\ &=\dfrac{11}{2}+\dfrac{12}{2}+\dfrac{13}{2}+\dfrac{14}{2}+\dfrac{15}{2}\\ &=\dfrac{11+12+13+14+15}{2}\\ &=\dfrac{65}{2}---(i)\end{align} L
- Question 9 Exercise 4.4
- \ G_3&=a_1 r^3=\dfrac{32}{9} \times \dfrac{27}{8}=12 \\ G_4&=a_1 r^4=\dfrac{32}{9} \times \dfrac{81}{1... {9} \times \dfrac{243}{32}=27\\ &\dfrac{16}{3},8,12,18,27\end{align} =====Question 9(ii)===== Insert
- Question 10 Exercise 4.4
- ign}b(b+48)&=(b+6)^2 \\ \Rightarrow b^2+48 b&=b^2+12 b+36 \\ \Rightarrow b^2+48 b-b^2-12 b&=36 \\ \Rightarrow 36 b&=36 \text { or } b=1\end{align} Putting
- Question 1 Exercise 4.5
- an. =====Question 1(i)===== Compute the sum $3+6+12+\ldots+3.2^9$ ====Solution==== In the given geome... &=\dfrac{2^4[2^7-1]}{2-1} \\ \Rightarrow S_7&=16(512-1)=2032.\end{align} =====Question 1(iv)===== Com
- Question 2 Exercise 4.5
- rac{1[(-2)^7-1]}{-2-1}\\ \Rightarrow S_7&=\dfrac{-128-1}{-3}\\ s_7&=\dfrac{129}{3}\end{align} =====Question 2(ii)===== Some of the components $a_1, a_n,