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- Question 2, Exercise 4.2 @math-11-nbf:sol:unit04
- lutions of Question 2 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... ==== Find the next three terms of each arithmetic sequence. $5,9,13, \ldots$ ** Solution. ** Give: $$5, 9,... 25 \end{align*} Thus, the next three terms of the sequence are $17$, $21$, $25$. =====Question 2(ii)===== Find the next three terms of each arithmetic sequence. $11,14,17, \ldots$ ** Solution. ** Given: $$11
- Question 1 and 2, Exercise 4.4 @math-11-nbf:sol:unit04
- s of Question 1 and 2 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... n. =====Question 1===== Determine whether each sequence is geometric. If so, find the common ratio. $5,20,100,500, \ldots$ ** Solution. ** Given sequence is $5, 20, 100, 500, \ldots $.\\ A sequence is geometric if any two of its consecutive terms have same rati
- Question 1, Exercise 4.2 @math-11-nbf:sol:unit04
- lutions of Question 1 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... ===== Find the first four terms of the arithmetic sequence with $a_{1}=4, d=3$ ** Solution. ** Given: $a_1= 4$, $d=3$.\\ The general term of an arithmetic sequence is: $$a_n = a_1 + (n - 1)d.$$ Now \begin{align*} ... ===== Find the first four terms of the arithmetic sequence with $a_1=7$, $d=5$ ** Solution. ** Given: $a_1
- Question 7 and 8, Exercise 4.2 @math-11-nbf:sol:unit04
- s of Question 7 and 8 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... kistan. =====Question 7===== Which term of the sequence $-6,-2,2, \ldots$ is $70$? ** Solution. ** Given $-6,-2,2, \ldots$ is an arithmetic sequence. Here $a_1=-6$, $d=-2+6=4$, $a_n=70$, $n=?$. The nth term of the arithmetic sequence is given as $$a_n=a_1+(n-1)d.$$ This gives \begin
- Question 3 and 4, Exercise 4.4 @math-11-nbf:sol:unit04
- s of Question 3 and 4 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... =====Question 3===== Determine whether the given sequence is geometric. If so, find the common ratio. $\fra... 8}, \frac{81}{16}, \ldots$ ** Solution. ** Given sequence is \(\frac{3}{2}, \frac{9}{4}, \frac{27}{8}, \fra... o consecutive terms has same ratio.\\ Hence given sequence is geometric and common ratio \(r = \frac{3}{2}\)
- Question 5 and 6, Exercise 4.2 @math-11-nbf:sol:unit04
- s of Question 5 and 6 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... kistan. =====Question 5===== Find an arithmetic sequence for $a_{17}=-40$ and $a_{28}=-73$, find $a_{1}$ and $d$. Write first five terms of the sequence. ** Solution. ** The nth term of the arithmetic sequence is given as $$a_n=a_1+(n-1)d$$ Given \begin{align
- Question 21 and 22, Exercise 4.1 @math-11-nbf:sol:unit04
- of Question 21 and 22 of Exercise 4.1 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... ict the general term or nth term, $a_{n}$, of the sequence. $\sqrt{2}, \sqrt{4}, \sqrt{6}, \sqrt{8}, \sqrt{10}, \ldots$ ** Solution. ** The given sequence is $$\sqrt{2}, \sqrt{4}, \sqrt{6}, \sqrt{8}, \sqr... ict the general term or nth term, $a_{n}$, of the sequence. $1.2,2.3,3.4,4.5, \ldots$ ** Solution. ** The g
- Question 3 and 4, Exercise 4.2 @math-11-nbf:sol:unit04
- s of Question 3 and 4 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... stion 3===== Find the 11th term of the arithmetic sequence $0.07,0.12,0.7, \ldots$ ** Solution. ** Given $... ==Question 4===== The third term of an arithmetic sequence is 14 and the ninth term is -1 . Find the first four terms of the sequence. ** Solution. ** Given: $a_3 = 14$ and $a_9 = -
- Question 8 and 9, Exercise 4.4 @math-11-nbf:sol:unit04
- s of Question 8 and 9 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... n 8===== Find the next two terms of the geometric sequence: $$90,30,10 \ldots$$ ** Solution. ** Given sequence is geometric with $a_1=90$ and $r=\dfrac{30}{90}=\dfr... n 9===== Find the next two terms of the geometric sequence: $$2,6,18 \ldots$$ ** Solution. ** Given seque
- Question 10 and 11, Exercise 4.4 @math-11-nbf:sol:unit04
- of Question 10 and 11 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... 10===== Find the next two terms of the geometric sequence: $$20,30,45 \ldots$$ ** Solution. ** Given sequence is geometric with \(a_1=20\) and \(r=\frac{30}{20}=\... 11===== Find the next two terms of the geometric sequence: $$729,243,81,\ldots$$ ** Solution. ** Given s
- Question 12 and 13, Exercise 4.4 @math-11-nbf:sol:unit04
- of Question 12 and 13 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... 12===== Find the next two terms of the geometric sequence: $$\frac{1}{27}, \frac{1}{9}, \frac{1}{3}, \ldots$$ ** Solution. ** Given sequence is geometric with \(a_1=\frac{1}{27}\) and \(r=\f... 13===== Find the next two terms of the geometric sequence: $$\frac{1}{4}, \frac{1}{2},-1, \ldots$$ ** Sol
- Unit 04: Sequences and Seeries @math-11-nbf:sol
- ====== Unit 04: Sequences and Seeries ====== This is a forth unit of the book "Model Textbook of Mathematics... tudents will be able to * Define an arithmetic sequence and find its general term. * Know arithmetic me... * Solve real life problems involving arithmetic sequence, arithmetic means and arithmetic series. * Define a geometric sequence and its general term. * Know geometric means be
- Question 19 and 20, Exercise 4.1 @math-11-nbf:sol:unit04
- of Question 19 and 20 of Exercise 4.1 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... ict the general term or nth term, $a_{n}$, of the sequence. $1,3,5,7,9, \ldots$ ** Solution. ** Given $$1, 3, 5, 7, 9, \ldots$$ This is arithmetic sequence with $a_1=1$, $d=3-1=2$. Thus $$a_n = a_1 + (n - ... ict the general term or nth term, $a_{n}$, of the sequence.$3,9,27,81,243, \ldots$ ** Solution. ** \begin{
- Question 5, 6 and 7, Exercise 4.4 @math-11-nbf:sol:unit04
- f Question 5, 6 and 7 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... 5===== Find the first four terms of the geometric sequence.$a_{1}=3, r=-2$ ** Solution. ** Given $a_{1}=3$... 6===== Find the first four terms of the geometric sequence. $a_{1}=27, r=-\frac{1}{3}$ ** Solution. ** Giv... 7===== Find the first four terms of the geometric sequence. $\quad a_{1}=12, r=\frac{1}{2}$ ** Solution. **
- Question 7 & 8, Exercise 4.6 @math-11-nbf:sol:unit04
- ons of Question 7 & 8 of Exercise 4.6 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mat... c{1}{10}, \frac{1}{13}, \ldots $ is an arithmetic sequence. Here, $ a_1 = \frac{1}{4} $, $d = \frac{1}{7} ... ====Question 8===== $7,4,1, \ldots$ is arithmetic sequence, find the 17th term in H.P. ** Solution. ** Given $7,4,1, \ldots$ is arithmetic sequence. Here $a_1=7$, $d=4-7=-3$, $n=17$. The general