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- Question 14, Exercise 4.5
- ====== Question 14, Exercise 4.5 ====== Solutions of Question 14 of Exercise 4.5 of Unit 04: Sequence and Series. This is u... deral Textbook Board, Islamabad, Pakistan. =====Question 14(i)===== Find fractional notation for the infin... d{align*} Hence $S_{\infty} =\dfrac{4}{9}$. =====Question 14(ii)===== Find fractional notation for the infi
- Question 1, Exercise 4.2
- ====== Question 1, Exercise 4.2 ====== Solutions of Question 1 of Exercise 4.2 of Unit 04: Sequence and Series. This is uni... eral Textbook Board, Islamabad, Pakistan. =====Question 1(i)===== Find the first four terms of the arithm... $a_1=4$, $a_2=7$, $a_3=10$, $a_4=13$. GOOD =====Question 1(ii)===== Find the first four terms of the arith
- Question 2, Exercise 4.2
- ====== Question 2, Exercise 4.2 ====== Solutions of Question 2 of Exercise 4.2 of Unit 04: Sequence and Series. This is uni... eral Textbook Board, Islamabad, Pakistan. =====Question 2(i)===== Find the next three terms of each arith... terms of the sequence are $17$, $21$, $25$. =====Question 2(ii)===== Find the next three terms of each arit
- Question 13, Exercise 4.2
- ====== Question 13, Exercise 4.2 ====== Solutions of Question 13 of Exercise 4.2 of Unit 04: Sequence and Series. This is u... eral Textbook Board, Islamabad, Pakistan. =====Question 13(i)===== Find A.M. between $7$ and $17$ ** Sol... = 12. \end{align*} Hence A.M. = $12$. GOOD =====Question 13(ii)===== Find A.M. between $3+3 \sqrt{2}$ and
- Question 14 and 15, Exercise 4.2
- ====== Question 14 and 15, Exercise 4.2 ====== Solutions of Question 14 and 15 of Exercise 4.2 of Unit 04: Sequence and Ser... deral Textbook Board, Islamabad, Pakistan. =====Question 14===== Find '$b$' if $10$ is A.M between $b$ and... > To get the answer given at the end of the book, question can be as follows: * Find '$b$' if $25$ is A.M
- 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 Unit 04: Sequence... deral Textbook Board, Islamabad, Pakistan. =====Question 17===== Find sum of the arithmetic series. $6+12+... gn} Hence the sum of given series is $1224$. =====Question 18===== Find sum of the arithmetic series. $34+30
- 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 Unit 04: Sequence... deral Textbook Board, Islamabad, Pakistan. =====Question 20===== Find the first three terms of the arithme... n} Hence $a_1=7$, $a_2=19$, $a_3=31$. =====Question 21===== Find the first three terms of each arithm
- 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: Sequence and S... deral Textbook Board, Islamabad, Pakistan. =====Question 5===== Find the first four terms of the geometric... a_1=3$, $a_2=-6$, $a_3=12$, $a_4=-24$. GOOD =====Question 6===== Find the first four terms of the geometric
- 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 Unit 04: Sequence... deral Textbook Board, Islamabad, Pakistan. =====Question 11===== Find $a_{1}$ for the geometric series: $S... s & a_1=4.\\ \end{align*} Hence $a_1=4$. =====Question 12===== Find $a_{1}$ for the geometric series: $S
- 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 Unit 04: Sequence... deral Textbook Board, Islamabad, Pakistan. =====Question 11===== Rewrite the sum using sigma notation: $-2... 16 - 32 + 64 = \sum_{k=1}^{6} (-1)^k 2^k $$ =====Question 12===== Rewrite the sum using sigma notation: $\f
- 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 Unit 04: Sequence... deral Textbook Board, Islamabad, Pakistan. =====Question 14===== Find the sum to $n$ terms of the series w... 1}^{\infty} T_{n}= \dfrac{n(n+3)}{2}$. GOOD =====Question 15===== Find the sum to $n$ terms of the series w
- Question 5 and 6, Exercise 4.8
- ====== Question 5 and 6, Exercise 4.8 ====== Solutions of Question 5 and 6 of Exercise 4.8 of Unit 04: Sequence and Series.... eral Textbook Board, Islamabad, Pakistan. =====Question 5===== Using the method of difference, find the s... } Hence, \( S_n = 2^n - 1 + 2n \). GOOD =====Question 6===== Using the method of difference, find the s
- 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: Sequence and Series.... eral Textbook Board, Islamabad, Pakistan. =====Question 3===== The $n$th term of the sequence is given, f... {11},\quad a_{15} = \frac{15}{16}.$ GOOD =====Question 4===== The $n$th term of the sequence is given, f
- Question 5 and 6, Exercise 4.1
- ====== Question 5 and 6, Exercise 4.1 ====== Solutions of Question 5 and 6 of Exercise 4.1 of Unit 04: Sequence and Series.... deral Textbook Board, Islamabad, Pakistan. =====Question 5===== The $n$th term of the sequence is given, f... = 8$, $a_{10} = 80$, $a_{15} = 195$. GOOD =====Question 6===== The $n$th term of the sequence is given, f
- Question 7 and 8, Exercise 4.1
- ====== Question 7 and 8, Exercise 4.1 ====== Solutions of Question 7 and 8 of Exercise 4.1 of Unit 04: Sequence and Series.... deral Textbook Board, Islamabad, Pakistan. =====Question 7===== The $n$th term of the sequence is given, f... -1}{512}$, $a_{15} = \frac{1}{16384}$. GOOD =====Question 8===== The $n$th term of the sequence is given, f