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- Question 1, Exercise 4.2
- ====== Question 1, Exercise 4.2 ====== Solutions of Question 1 of Exercise 4.2 of Unit 04: Sequence and Seri... f the arithmetic sequence with $a_{1}=4, d=3$ ** Solution. ** Given: $a_1= 4$, $d=3$.\\ The general term o... f the arithmetic sequence with $a_1=7$, $d=5$ ** Solution. ** Given: $a_1= 7$, $d=5$.\\ The general term o... each arithmetic sequence. $a_{1}=16$, $d=-2$. ** Solution. ** Given: $a_1= 16$, $d=-2$.\\ We have $$a_n =
- Question 14, Exercise 4.5
- ====== Question 14, Exercise 4.5 ====== Solutions of Question 14 of Exercise 4.5 of Unit 04: Sequence and Se... for the infinite geometric series; $0.444...$ ** Solution. ** We can express the decimal as $$0.444... = 0... the infinite geometric series; $9.99999 ...$ ** Solution. ** We can express the decimal as $$0.99999 ... ... he infinite geometric series; $0.5555 \ldots$ ** Solution. ** We can express the decimal as $$0.5555 \ldot
- Question 2, Exercise 4.2
- ====== Question 2, Exercise 4.2 ====== Solutions of Question 2 of Exercise 4.2 of Unit 04: Sequence and Seri... of each arithmetic sequence. $5,9,13, \ldots$ ** Solution. ** Give: $$5, 9, 13, \ldots $$ Thus $a_1=5$, $d... each arithmetic sequence. $11,14,17, \ldots$ ** Solution. ** Given: $$11, 14, 17, \ldots$$ Thus $a_1=11$,... ac{1}{2}, \dfrac{3}{2}, \dfrac{5}{2}, \ldots$ ** Solution. ** The given sequence is $$\frac{1}{2}, \frac{
- Question 13, Exercise 4.2
- ====== Question 13, Exercise 4.2 ====== Solutions of Question 13 of Exercise 4.2 of Unit 04: Sequence and Se... ion 13(i)===== Find A.M. between $7$ and $17$ ** Solution. ** Here $a=7$ and $b=17$.\\ Now \begin{align*} ... .M. between $3+3 \sqrt{2}$ and $7-3 \sqrt{2}$ ** Solution. ** Here $a=3+3\sqrt{2}$ and $b=7-3\sqrt{2}$.\\ ... Find A.M. between $7 \sqrt{5}$ and $\sqrt{5}$ ** Solution. ** Here $a=7\sqrt{5}$ and $b=\sqrt{5}$.\\ Now \b
- Question 13, 14 and 15, Exercise 4.8
- ===== Question 13, 14 and 15, Exercise 4.8 ====== Solutions of Question 13, 14 and 15 of Exercise 4.8 of Uni... ac{1}{9 \cdot 15}+\ldots \ldots$ to $n$ term. ** Solution. ** Let $T_k$ represent the $k$th term of the ser... ac{1}{2k+9} \right). \end{align*} <fc #ff0000>The solution seems very lengthy, it will be solved later.</fc>... ies: $\sum_{k=1}^{n} \frac{1}{9 k^{2}+2 k-2}$ ** Solution. ** =====Question 15===== Evaluate the sum of
- Question 9 and 10, Exercise 4.3
- ====== Question 9 and 10, Exercise 4.3 ====== Solutions of Question 9 and 10 of Exercise 4.3 of Unit 04: Seq... the sum of the odd numbers from $1$ to $99$. ** Solution. ** ** Solution. ** Sum of the odd numbers from $1$ to $99$ is $$1+3+5+...+99 (50 \text{ terms}).$$ This ... ltiples of 4 that are between $14$ and $523$. ** Solution. ** Sum of all multiples of 4 that are between $
- Question 17, 18 and 19, Exercise 4.3
- ===== Question 17, 18 and 19, Exercise 4.3 ====== Solutions of Question 17, 18 and 19 of Exercise 4.3 of Uni... f the arithmetic series. $6+12+18+\ldots+96$. ** Solution. ** Given arithmetic series: $$6+12+18+\ldots+9... of the arithmetic series. $34+30+26+\ldots+2$ ** Solution. ** Given arithmetic series: $$34+30+26+\ldots+2... e arithmetic series. $10+4+(-2)+\ldots+(-50)$ ** Solution. ** Given arithmetic series: $$10+4+(-2)+\ldots
- Question 20, 21 and 22, Exercise 4.3
- ===== Question 20, 21 and 22, Exercise 4.3 ====== Solutions of Question 20, 21 and 22 of Exercise 4.3 of Uni... series. $a_{1}=7$, $a_{n}=139$, $S_{n}=876$. ** Solution. ** Given $a_{1}=7$, $a_{n}=139$, $S_{n}=876$. F... metic series. $n=14$, $a_{n}=53$, $S_{n}=378$ ** Solution. ** Given $n=14$, $a_{n}=53$, $S_{n}=378$. First... series. $a_{1}=6$, $a_{n}=306$, $S_{n}=1716$. ** Solution. ** Given $a_{1}=6$, $a_{n}=306$, $S_{n}=1716$.
- Question 5, 6 and 7, Exercise 4.4
- ====== Question 5, 6 and 7, Exercise 4.4 ====== Solutions of Question 5, 6 and 7 of Exercise 4.4 of Unit 04:... rms of the geometric sequence.$a_{1}=3, r=-2$ ** Solution. ** Given $a_{1}=3$ and $r=-2$. Use the formula ... eometric sequence. $a_{1}=27, r=-\frac{1}{3}$ ** Solution. ** Given $a_{1}=27$ and $r=-\frac{1}{3}$. Use t... ric sequence. $\quad a_{1}=12, r=\frac{1}{2}$ ** Solution. ** Given $a_{1}=12$ and $r=\frac{1}{2}$. Use th
- Question 20 and 21, Exercise 4.4
- ====== Question 20 and 21, Exercise 4.4 ====== Solutions of Question 20 and 21 of Exercise 4.4 of Unit 04: S... means. $$3 , \_\_\_ , \_\_\_ , \_\_\_ , 48$$ ** Solution. ** We have given $a_1=3$ and $a_5=48$. Assume ... <callout type="warning" icon="true"> **The good solution is as follows:** We have given $a_1=3$ and $a_5=... ing geometric means. $$1 ,\_\_\_,\_\_\_, 8$$ ** Solution. ** We have $a_1=1$ and $a_4=8$. Assume $r$ to b
- Question 11, 12 and 13, Exercise 4.5
- ===== Question 11, 12 and 13, Exercise 4.5 ====== Solutions of Question 11, 12 and 13 of Exercise 4.5 of Uni... the geometric series: $S_{n}=244, r=-3, n=5$ ** Solution. ** Given: $S_{n}=244$, $r=-3$, $n=5$.\\ We know... or the geometric series: $S_{n}=32, r=2, n=6$ ** Solution. ** Given: $S_{n}=32$, $r=2$, $n=6$.\\ We know $... geometric series: $a_{n}=324, r=3, S_{n}=484$ ** Solution. ** Given: $a_{n}=324$, $r=3$, $S_{n}=484$. As
- Question 11, 12 and 13, Exercise 4.7
- ===== Question 11, 12 and 13, Exercise 4.7 ====== Solutions of Question 11, 12 and 13 of Exercise 4.7 of Uni... e sum using sigma notation: $-2+4-8+16-32+64$ ** Solution. ** $$ -2 + 4 - 8 + 16 - 32 + 64 = \sum_{k=1}^{6... 3}+\frac{1}{3 \cdot 4}+\frac{1}{4 \cdot 5}+$ ** Solution. ** $$ \frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3}... ^{3}=\left[\frac{n(n+1)}{2}\right]^{3}$ FIXME ** Solution. ** ====Go to ==== <text align="left"><b
- Question 14, 15 and 16, Exercise 4.7
- ===== Question 14, 15 and 16, Exercise 4.7 ====== Solutions of Question 14, 15 and 16 of Exercise 4.7 of Uni... erms of the series whose $n$th term is $n+1$. ** Solution. ** Consider $T_n$ represents the $n$th term of ... the series whose $n$th term is $n^{2}+2 n$. ** Solution. ** Consider $T_k$ represents the $k$th term of ... dsymbol{n}$ th term is given: $3 n^{2}+2 n+1$ ** Solution. ** Consider $T_k$ represents the $k$th term of
- Question 1 and 2, Exercise 4.1
- ====== Question 1 and 2, Exercise 4.1 ====== Solutions of Question 1 and 2 of Exercise 4.1 of Unit 04: Seque... and the 15 th term: $a_{15}$. $$a_{n}=3 n+1$$ ** Solution. ** Given $$a_{n}=3 n+1$$ Then \begin{align*} a_... and the 15 th term, $a_{15}$. $$a_{n}=3 n-1$$ ** Solution. ** Given: $$a_{n}=3 n-1.$$ Then \begin{align*} a
- Question 3 and 4, Exercise 4.1
- ====== Question 3 and 4, Exercise 4.1 ====== Solutions of Question 3 and 4 of Exercise 4.1 of Unit 04: Seque... 0}$ and the 15 th term: $a_{n}=\frac{n}{n+1}$ ** Solution. ** Given $$a_n = \frac{n}{n+1}.$$ Then \begin{al... and the 15 th term: $a_{15}$.$a_{n}=n^{2}+1$ ** Solution. ** Do yourself. ====Go to ==== <text align