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- Question 3 and 4 Exercise 4.1
- s of Question 3 and 4 of Exercise 4.1 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... =Question 3(i)==== Write down the nth term of the sequence as suggested by the pattern. 12,\dfra...… ====Solution==== We can reform the given sequence to pick the pattern of the sequence as: $$\dfrac{1}{1+1}, \dfrac{2}{2+1}, \dfrac{3}{3+1}, \dfrac{4}{4+1},..
- Question 1 and 2 Exercise 4.1
- s of Question 1 and 2 of Exercise 4.1 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... 4,6,8, \ldots ,50$ ====Solution==== It is finite sequence whose last term is 50. =====Question 1(ii)===... 0,1,0,1, \ldots$. ====Solution==== It is infinite sequence, the last term may be 0 or 1 , but how much terms in this sequence, we don't know. =====Question 1(iii)===== Classi
- Question 6 Exercise 4.1
- lutions of Question 6 of Exercise 4.1 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... ldots.$$ =====Question 6(i)===== Find the Pascal sequence for n=5 by using its general recursive definiti... GOOD ====Solution==== For n=5, we have Pascal sequence as follows: $$P_0=1, P_{r+1}=\dfrac{5-r}{r+1} P_r... nd{align} So, 0=P7=P8=.... Hence the Pascal sequence for n=5 is 1,5,10,10,5,1,0,0,0,…. ====
- Question 1 Exercise 4.4
- lutions of Question 1 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... ===== Write the first five terms of geometric ric sequence given that a1=5,r=3 ====Solution==== The gcometric sequence is $a_1, a_1 r, a_1 r^2, a_1 r^3, a_1 r^4, \ldots... ===== Write the first five terms of geometric ric sequence given that a1=8,r=−12 ====Sol
- Question 4 & 5 Exercise 4.4
- ons of Question 4 & 5 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... on 4===== How many terms are there in a geometric sequence in which the first and the last terms are 16 and ... dfrac{1}{2}$ ? ====Solution==== First term of the sequence a1=16\\ Last term of the sequence an=164 Common ratio r=12\\ We have to find $n
- Question 6 & 7 Exercise 4.4
- ons of Question 6 & 7 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... w that the reciprocal of the terms of a geometric sequence also form a geometric sequence. ====Solution==== Let we are considering the standard geometric sequence with common ratio r that is\\ $$a_1, a_1 r, a_1
- Question 5 and 6 Exercise 4.2
- s of Question 5 and 6 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... ar, Pakistan. =====Question 5===== Show that the sequence $$\log a, \log (a b), \log \left(a b^2\right), \l... on==== We first find nth term. Each term of the sequence is log of some number. Each log contains a b... an=log(abn−1). We show that the given sequence is A.P. Since \begin{align}a_n&=\log(a b^{n-1}).
- Question 1 and 2 Exercise 4.2
- s of Question 1 and 2 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... ion 1===== Find the 15th term of the arithmetic sequence 2,5,8,… GOOD ====Solution==== Here $a_1=2... 2=44 \end{align} Hence the 15th term of the given sequence is 44. =====Question 2===== The first term of an arithmetic sequence is 8 and the 21st is 108. Find the 7th term. GOOD
- Question 11 & 12 Exercise 4.3
- s of Question 11 & 12 of Exercise 4.3 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... econd a3=80ft and so on.\\ Hence the sequence 16,48,80,… is an arithmetic sequence with d=48−16=32.\\ The total distance in six second is... d day}&=Rs. 3 \text{ and so on}\end{align} So the sequence formed 1,2,3,4,… is an arithmetic sequenc
- Question 2 & 3 Exercise 4.4
- ons of Question 2 & 3 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... 2===== Suppose that the third term of a geometric sequence is 27 and the fifth term is 243. Find the first term and common ratio of the sequence. ====Solution==== Here $$a_3=27 \quad\text{and}\q... ion 3===== Find the seventh term of the geometric sequence that has 2 and −√2 for its second and t
- Question 2 Exercise 4.5
- lutions of Question 2 of Exercise 4.5 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... onents a1,an,n2r and Sn of a geometric sequence are given. Find the ones that are missing a1=1,...onentsa_1, a_n, n_2 randS_n$ of a geometric sequence are given. Find the ones that are missing r=\dfr...onentsa_1, a_n, n_2 randS_n$ of a geometric sequence are given. Find the ones that are missing $r=-2,
- Question 3 and 4 Exercise 4.2
- s of Question 3 and 4 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... 25.GOOD=====Question4=====Then$th term of sequence is given by an=2n+7. Show that it is an arithm... -7=2\end{align} This gives every two terms of the sequence has same distance 2, hence it is an A.P. Putt
- Question 1 Exercise 4.3
- lutions of Question 1 of Exercise 4.3 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... um of the indicated number of terms in arithmetic sequence: 9,7,5,3,…; 20th term; 20 terms. GOOD ===... e indicated number of terms in case of arithmetic sequence: 3,83,73,2,…; 11th
- Question 9 Exercise 4.4
- lutions of Question 9 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... _2, G_3, G_4, G_5, \dfrac{81}{2}$ forms geometric sequence of 7 terms, with a7=812 and a1=\df...3,G4,G5,G6,−764 forms geometric sequence of 8 terms, with\\ \begin{align}a_8&=-\dfrac{7}
- Question 3 Exercise 4.5
- lutions of Question 3 of Exercise 4.5 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathema... t five terms and the sum of an infinite geometric sequence having a2=2 and a3=1\\ ====Solution==== We ... }{4} \text {. }\end{align} The infinite geometric sequence is:\\ $$4,2,1, \dfrac{1}{2}, \dfrac{1}{4}, \ldots