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- Question 1, Exercise 4.2
- , Islamabad, Pakistan. =====Question 1(i)===== Find the first four terms of the arithmetic sequence w... a_3=10$, $a_4=13$. GOOD =====Question 1(ii)===== Find the first four terms of the arithmetic sequence w... 3=17$, $a_4=22$. GOOD =====Question 1(iii)===== Find the first four terms of each arithmetic sequence.... _3=12$, $a_4=10$. GOOD =====Question 1(iv)===== Find the first four terms of the arithmetic sequence.
- Question 20, 21 and 22, Exercise 4.3
- ard, Islamabad, Pakistan. =====Question 20===== Find the first three terms of the arithmetic series. $... ven $a_{1}=7$, $a_{n}=139$, $S_{n}=876$. First we find $n$ and $d$.\\ As \begin{align} &S_n=\frac{n}{2}[... $a_2=19$, $a_3=31$. =====Question 21===== Find the first three terms of each arithmetic series. ... Given $n=14$, $a_{n}=53$, $S_{n}=378$. First we find $a_1$ and $d$.\\ As \begin{align} &S_n=\frac{n}{2
- Question 5 and 6, Exercise 4.5
- ard, Islamabad, Pakistan. =====Question 5===== Find the sum of the geometric series. $a_{1}=7, r=2, n... $a_1 = 7$, $r = 2$ and $n = 14$. The formula to find the sum of $n$ terms of a geometric series is\\ $... e required sum is $114681$. =====Question 6===== Find the sum of the geometric series. $a_{1}=12, a_{5}... = -3$.\\ Now, we can use \(r = -3\) (as given) to find the number of terms, \(n\): To find $n$, we use $
- Question 14, Exercise 4.5
- , Islamabad, Pakistan. =====Question 14(i)===== Find fractional notation for the infinite geometric se... infty} =\dfrac{4}{9}$. =====Question 14(ii)===== Find fractional notation for the infinite geometric se... e $S_{\infty}= 1 $. =====Question 14(iii)===== Find fractional notation for the infinite geometric se... nfty}= \frac{5}{9}.$ =====Question 14(iv)===== Find fractional notation for the infinite geometric se
- Question 2, Exercise 4.2
- , Islamabad, Pakistan. =====Question 2(i)===== Find the next three terms of each arithmetic sequence.... e are $17$, $21$, $25$. =====Question 2(ii)===== Find the next three terms of each arithmetic sequence.... are $20$, $23$, $26$. =====Question 2(iii)===== Find the next three terms of each arithmetic sequence.... {2}, \frac{3}{2}, \frac{5}{2}, \ldots$$ First, we find the common difference: \begin{align*} d &= \frac{
- Question 13, Exercise 4.2
- Islamabad, Pakistan. =====Question 13(i)===== Find A.M. between $7$ and $17$ ** Solution. ** Here ... ence A.M. = $12$. GOOD =====Question 13(ii)===== Find A.M. between $3+3 \sqrt{2}$ and $7-3 \sqrt{2}$ *... ence A.M. = $5$. GOOD =====Question 13(iii)===== Find A.M. between $7 \sqrt{5}$ and $\sqrt{5}$ ** Solu... = $ 4 \sqrt{5}$. GOOD =====Question 13(iv)===== Find A.M. between $2y+5$ and $5y+3$ ** Solution. ** H
- Question 14 and 15, Exercise 4.2
- ard, Islamabad, Pakistan. =====Question 14===== Find '$b$' if $10$ is A.M between $b$ and $20$. ** S... end of the book, question can be as follows: * Find '$b$' if $25$ is A.M between $b$ and $20$. * Find '$b$' if $10$ is A.M between $b$ and $-10$. </callout> =====Question 15===== Find $x$ and $y$ if $2$ and $13$ are two arithmetic me
- Question 3 and 4, Exercise 4.3
- oard, Islamabad, Pakistan. =====Question 3===== Find the sum of each series. $a_{1}=5$, $a_{n}=100$, $n=200$ FIXME Statement is logically incorrect. Find the sum of arithmetic series with: $a_{1}=5$, $a_... ence $S_{200}=10500$. GOOD =====Question 4===== Find the sum of series. $a_{1}=4$, $n=15$, $d=3$. FIXME Statement is logically incorrect. Find the sum of arithmetic series with: $a_{1}=4$, $n=
- Question 22 and 23, Exercise 4.4
- ard, Islamabad, Pakistan. =====Question 22===== Find the missing geometric means. $$8 , \_\_\_, \_\_\_... plies r &= \frac{1}{2}. \end{align*} Thus, we can find the missing terms: \begin{align*} a_2 &= a_1 r = ... , $1$, and $d\frac{1}{2}$. =====Question 23===== Find the missing geometric means. $$3 , \_\_\_ , 75$$... 25 \\ \implies r &= 5. \end{align*} Thus, we can find the missing terms: \begin{align*} a_2 &= a_1 r =
- Question 24 and 25, Exercise 4.4
- ard, Islamabad, Pakistan. =====Question 24===== Find the missing geometric means. $$5 , \_\_\_, \_\_\... 16 \\ \implies r &= 2. \end{align*} Thus, we can find the missing terms: \begin{align*} a_2 &= a_1 r = ... are $10$, $20$, and $40$. =====Question 25===== Find the missing geometric means. $$7 ,\_\_\_, \_\_\_,... 16 \\ \implies r &= 2. \end{align*} Thus, we can find the missing terms: \begin{align*} a_2 &= a_1 r =
- Question 3 and 4, Exercise 4.5
- oard, Islamabad, Pakistan. =====Question 3===== Find the sum of geometric series with $a_{1}=5$, $r=3$... Given: $a_{1}=5$, $r=3$, $n=12$ The formula to find the sum of $n$ terms of geometric series \[ S_n =... ired sum is $1328600$. =====Question 4===== Find the sum of the geometric series. $a_{1}=256, r=0.... = 256$, $r = 0.75$ and $n = 9$. The formula to find the sum of $n$ terms of a geometric series is\\ $
- Question 7 and 8, Exercise 4.5
- ard, Islamabad, Pakistan. =====Question 7===== Find the sum of the geometric series. $a_{1}=16, r=-\f... , $r = -\frac{1}{2}$ and $n = 10$. The formula to find the sum of $n$ terms of a geometric series is\\ $... pproximately $10.67$ GOOD =====Question 8===== Find the sum of the geometric series. $a_{1}=243, r=-\... $r = -\frac{2}{3}$, and $n = 5$. The formula to find the sum of $n$ terms of a geometric series is $$S
- Question 5 and 6, Exercise 4.2
- oard, Islamabad, Pakistan. =====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 se... n arithmetic sequence is 19 and 11 th term is 43. Find the first term and 87 th term. ** Solution. **
- Question 1 and 2, Exercise 4.3
- ard, Islamabad, Pakistan. =====Question 1===== Find the sum of series: $4+7+10+13+16+19+22+25$ ** So... of given series is 116. GOOD =====Question 2===== Find the sum of series. $a_{1}=2$, $a_{n}=200$, $n=100$ FIXME Statement is logically incorrenct. Find the sum of arithematic series with: $a_{1}=2$, $a
- Question 5 and 6, Exercise 4.3
- oard, Islamabad, Pakistan. =====Question 5===== Find the sum of series. $a_{1}=50$, $n=20$, $d=-4$. FIXME Statement is logically incorrect. Find the sum of arithmetic series with: $a_{1}=50$, $n... } Hence $S_{20}=240$. GOOD =====Question 6===== Find the sum of series. $-3+(-7)+(-11)+\cdots +a_{10}$