Search
You can find the results of your search below.
Matching pagenames:
- Question 1 and 2 Exercise 4.1
- Question 3 and 4 Exercise 4.1
- Question 5 Exercise 4.1
- Question 6 Exercise 4.1
- Question 1 and 2 Exercise 4.2
- Question 3 and 4 Exercise 4.2
- Question 5 and 6 Exercise 4.2
- Question 7 Exercise 4.2
- Question 8 Exercise 4.2
- Question 9 Exercise 4.2
- Question 10 Exercise 4.2
- Question 11 Exercise 4.2
- Question 12 & 13 Exercise 4.2
- Question 14 Exercise 4.2
- Question 15 Exercise 4.2
- Question 16 Exercise 4.2
- Question 17 Exercise 4.2
- Question 1 Exercise 4.3
- Question 2 Exercise 4.3
- Question 3 & 4 Exercise 4.3
- Question 5 & 6 Exercise 4.3
- Question 7 & 8 Exercise 4.3
- Question 9 & 10 Exercise 4.3
- Question 11 & 12 Exercise 4.3
- Question 13 & 14 Exercise 4.3
- Question 1 Exercise 4.4
- Question 2 & 3 Exercise 4.4
- Question 4 & 5 Exercise 4.4
- Question 6 & 7 Exercise 4.4
- Question 8 Exercise 4.4
- Question 9 Exercise 4.4
- Question 10 Exercise 4.4
- Question 11 Exercise 4.4
- Question 12 Exercise 4.4
- Question 1 Exercise 4.5
- Question 2 Exercise 4.5
- Question 3 Exercise 4.5
- Question 4 Exercise 4.5
- Question 5 & 6 Exercise 4.5
- Question 7 & 8 Exercise 4.5
- Question 9 & 10 Exercise 4.5
- Question 11 & 12 Exercise 4.5
- Question 13 & 14 Exercise 4.5
- Question 15 & 16 Exercise 4.5
Fulltext results:
- 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: ... nd infinite sequences\\ $2,4,6,8, \ldots ,50$ ====Solution==== It is finite sequence whose last term i... and infinite sequences. $1,0,1,0,1, \ldots$. ====Solution==== It is infinite sequence, the last term m... nfinite sequences: $...,-4,0,4,8, \ldots, 60$ ====Solution==== This is infinite sequence. =====Questio
- 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: ... rac{2}{3} \dfrac{3}{4}, \dfrac{4}{5}, \ldots$ ====Solution==== We can reform the given sequence to pick... gested by the pattern. $2,-4,6,-8,10, \ldots$ ====Solution==== We can reform the given sequence to pick... suggested by the pattern. $1,-1,1,-1, \ldots$ ====Solution==== We can reform the give sequence to pick
- Question 12 & 13 Exercise 4.2
- ====== Question 12 & 13 Exercise 4.2 ====== Solutions of Question 12 & 13 of Exercise 4.2 of Unit 04: ... ry during his twenty first year of work? GOOD ====Solution==== Suppose $a_1$ represents salary of worke... e arithmetic mean between $12$ and $18$. GOOD ====Solution==== Here $a=12, b=18$.\\ Let say $A$ be arit... an between $\dfrac{1}{3}$ and $\dfrac{1}{4}$. ====Solution==== Here $a=\dfrac{1}{3}, b=\dfrac{1}{4}$,\\
- Question 1 Exercise 4.5
- ====== Question 1 Exercise 4.5 ====== Solutions of Question 1 of Exercise 4.5 of Unit 04: Sequence and... i)===== Compute the sum $3+6+12+\ldots+3.2^9$ ====Solution==== In the given geometric series: $a_1=3, \... Compute the sum $8+4+2+\ldots+\dfrac{1}{16}$ ====Solution==== In the give geometric series $$a_1=8, \q... = Compute the sum $2^4+2^5+2^6+\ldots+2^{10}$ ====Solution==== In the give geometric series.\\ $$a_1=2^
- Question 5 Exercise 4.1
- ====== Question 5 Exercise 4.1 ====== Solutions of Question 5 of Exercise 4.1 of Unit 04: Sequence and... eries in expanded form, $\sum_{j=1}^6(2 j-3)$ ====Solution==== \begin{align}\sum_{j=1}^6(2 j-3)&=(2.1-3... n expanded form, $\sum_{k=1}^5(-1)^k 2^{k-1}$ ====Solution==== \begin{align}\sum_{k=1}^5(-1)^k 2^{k-1}&... ed form, $\sum_{j=1}^{\infty} \dfrac{1}{2^j}$ ====Solution==== \begin{align}\sum_{j=1}^{\infty} \dfrac{
- Question 2 Exercise 4.3
- ====== Question 2 Exercise 4.3 ====== Solutions of Question 2 of Exercise 4.3 of Unit 04: Sequence and... one that is missing: $a_1=2, n=17, d=3$. GOOD ====Solution==== Given: $a_1=2, n=17, d=3$ \\ We need to ... that are missing $a_1=-40, S_{21}=210$. GOOD ====Solution==== Given: $a_1=-40$ and $S_{21}=210$.\\ So ... that are missing $a_1=-7, d=8, S_n=225$. GOOD ====Solution==== Given: $a_1=-7, d=8, S_n=225$, we have t
- Question 8 Exercise 4.4
- ====== Question 8 Exercise 4.4 ====== Solutions of Question 8 of Exercise 4.4 of Unit 04: Sequence and... Find the geometric mean of $3.14$ and $2.71$ ====Solution==== Here $a=3.14$ and $b=2.71$\\ then $$G= \... == Find the geometric mean of $-6$ and $-216$ ====Solution==== Here $a=-6$ and $b=-216$ then\\ \begin{a... == Find the geometric mean of $x+y$ and $x-y$ ====Solution==== Here $a=x+y$ and $b=x-y$\\ then $$G= \pm
- Question 4 Exercise 4.5
- ====== Question 4 Exercise 4.5 ====== Solutions of Question 4 of Exercise 4.5 of Unit 04: Sequence and... decimal to common fraction $0 . \overline{8}$ ====Solution==== We can write $$0 . \overline{8}=0.888888... ecimal to common fraction $1 . \overline{63}$ ====Solution==== Since \begin{align}1 . \overline{63}&=1+... ecimal to common fraction $2 . \overline{15}$ ====Solution==== Since \begin{align}2 . \overline{15}&=2+
- Question 1 Exercise 4.4
- ====== Question 1 Exercise 4.4 ====== Solutions of Question 1 of Exercise 4.4 of Unit 04: Sequence and... ic ric sequence given that $a_1=5, \quad r=3$ ====Solution==== The gcometric sequence is $a_1, a_1 r, a... nce given that $a_1=8, \quad r=-\dfrac{1}{2}$ ====Solution==== The geomerric sequence is $a_1, a_1 r, a... t $a_1=-\dfrac{9}{16}, \quad r=-\dfrac{2}{3}$ ====Solution==== The geometric sequence is $a_1, a_1 r, a
- Question 2 Exercise 4.5
- ====== Question 2 Exercise 4.5 ====== Solutions of Question 2 of Exercise 4.5 of Unit 04: Sequence and... re missing $a_1=1, \quad r=-2, \quad a_n=64$. ====Solution==== We first find $n$ and then $S_n$\\ We kn... that are missing $r=\dfrac{1}{2}, a_9=1, n=9$ ====Solution==== We first find $a_1$ and then $S_9$.\\ W... nes that are missing $r=-2, S_n=-63, a_n=-96$ ====Solution==== We know that\\ \begin{align}S_n&=\dfrac{
- Question 6 Exercise 4.1
- ====== Question 6 Exercise 4.1 ====== Solutions of Question 6 of Exercise 4.1 of Unit 04: Sequence and ... using its general recursive definition. GOOD ====Solution==== For $n=5$, we have Pascal sequence as f... 6$ by using its general recursive definition. ====Solution==== As we know the general definition of Pas... $ by using its general recursive definition. =====Solution===== As we know the general definition of Pa
- Question 3 and 4 Exercise 4.2
- ====== Question 3 and 4 Exercise 4.2 ====== Solutions of Question 3 and 4 of Exercise 4.2 of Unit 04: ... arithmetic progression $6,9,12, \ldots, 78$. ====Solution==== Here $a_1=6$ and $d=9-6=3$ and $a_n=78$.... ithmetic progression. Also find its 7th term. ====Solution==== Given that $$a_n=2 n+7. --- (1)$$ Then \... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4-2-p1 |< Question 1 & 2]]</btn></text>
- Question 5 and 6 Exercise 4.2
- ====== Question 5 and 6 Exercise 4.2 ====== Solutions of Question 5 and 6 of Exercise 4.2 of Unit 04: ... , \ldots$$ is an A.P. Also find its nth term. ====Solution==== We first find $n$th term. Each term of t... k-4$ are in A.P. Also find the sequence. GOOD ====Solution==== Since the given terms are in A.P, \begin... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4-2-p2 |< Question 3 & 4]]</btn></text>
- Question 14 Exercise 4.2
- ====== Question 14 Exercise 4.2 ====== Solutions of Question 14 of Exercise 4.2 of Unit 04: Sequence a... three arithmetic means between 6 and 41. GOOD ====Solution==== Let $A_1, A_2, A_3$ be three arithmetic ... four arithmetic means between 17 and 32. GOOD ====Solution==== Let $A_1, A_2, A_3, A_4$ be four arithme... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4-2-p9 |< Question 12 & 13 ]]</btn></tex
- Question 3 & 4 Exercise 4.3
- ====== Question 3 & 4 Exercise 4.3 ====== Solutions of Question 3 & 4 of Exercise 4.3 of Unit 04: Sequ... ers divisible by $5$ from $25$ to $350$. GOOD ====Solution==== The numbers divisible by $5$ from $25$ t... the sum of their cubes is $6336$ . Find them. ====Solution==== Let us suppose the three numbers are $a-... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4-3-p2 |< Question 2 ]]</btn></text> <te