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- Question 2 Exercise 4.3
- components $a_1, a_n, n, d$ and $S_n$ are given. Find the one that is missing: $a_1=2, n=17, d=3$. GOOD... ution==== Given: $a_1=2, n=17, d=3$ \\ We need to find $a_{17}$ and $S_{17}$. As we know $$a_{n}=a_1+(n-... components $a_1, a_n, n, d$ and $S_n$ are given. Find the one that are missing $a_1=-40, S_{21}=210$. G... $S_{21}=210$.\\ So we have $n=21$ and we have to find $a_{21}$ and $d$. As \begin{align}&S_{21}=\dfrac{
- Question 12 & 13 Exercise 4.2
- =750$. The given problem is of A.P and we have to find $a_{21}$. As, we have \begin{align} a_{21}&=a_1+... is dollars 18,500. GOOD =====Question 13(i)===== Find the arithmetic mean between $12$ and $18$. GOOD =... etween 12 and 18. GOOD =====Question 13(ii)===== Find the arithmetic mean between $\dfrac{1}{3}$ and $\... }{24}\end{align} GOOD =====Question 13(iii)===== Find the arithmetic mean between $-6,-216$. GOOD ====S
- Question 2 Exercise 4.5
- 2 r$ and $S_n$ of a geometric sequence are given. Find the ones that are missing $a_1=1, \quad r=-2, \quad a_n=64$. ====Solution==== We first find $n$ and then $S_n$\\ We know $a_n=a_1 r^{n-1}$, t... 2 r$ and $S_n$ of a geometric sequence are given. Find the ones that are missing $r=\dfrac{1}{2}, a_9=1, n=9$ ====Solution==== We first find $a_1$ and then $S_9$.\\ We know $$a_9=a_1 r^8$$\
- Question 1 and 2 Exercise 4.1
- === This finite sequence. =====Question 2(i)==== Find first four terms of the sequence with the given g... equence are $1,3,6, 10$. =====Question 2(ii)==== Find first four terms of the sequence with the given g... ence are $4,-8,16,-32$. =====Question 2(iii)==== Find first four terms of the sequence with the given g... ac{1}{27},\dfrac{1}{81}$. =====Question 2(iv)==== Find first four terms of the sequence with the given g
- Question 5 and 6 Exercise 4.2
- \log \left(a b^3\right), \ldots$$ is an A.P. Also find its nth term. ====Solution==== We first find $n$th term. Each term of the sequence is $\log$ of some nu... en sequence is in A.P. GOOD =====Question 6===== Find the value of $k$, if $2 k+7,6 k-2$, $8 k-4$ are in A.P. Also find the sequence. GOOD ====Solution==== Since the giv
- Question 8 Exercise 4.4
- TBB) Peshawar, Pakistan. =====Question 8(i)===== Find the geometric mean of $3.14$ and $2.71$ ====Solut... \text{or} \quad -2.94$$ =====Question 8(ii)===== Find the geometric mean of $-6$ and $-216$ ====Solutio... \text{or} \quad -36$$ =====Question 8(iii)===== Find the geometric mean of $x+y$ and $x-y$ ====Solutio... = \pm \sqrt{x^2-y^2}$$ =====Question 8(iv)===== Find the geometric mean of $\sqrt{2}+3$ and $\sqrt{2}-
- Question 6 Exercise 4.1
- re } r=0,1,2,3,\ldots.$$ =====Question 6(i)===== Find the Pascal sequence for $n=5$ by using its genera... ,10,5,1,0,0,0, \ldots$. =====Question 6(ii)===== Find the Pascal sequence for $n=6$ by using its genera... ,15,6,1,0,0,0,\ldots$. =====Question 6(iii)===== Find the Pascal sequence for $n=8$ by using its genera
- Question 3 & 4 Exercise 4.3
- KPTBB) Peshawar, Pakistan. =====Question 3===== Find sum of all the numbers divisible by $5$ from $25$... his is A.P. with $a_1=25, d=5$ and $a_n=350$\\ To find $n$, we know that \begin{align}a_n&=a_1+(n-1) d\e... ce is $36$ and the sum of their cubes is $6336$ . Find them. ====Solution==== Let us suppose the three n
- Question 1 Exercise 4.5
- uad r=\dfrac{6}{3}=2$ and $a_n=3.2^9$.\\ We first find $n$ and then the sum of series.\\ We know that $$... } \quad$$\\ and $$a_n=\dfrac{1}{16}$$.\\ We first find $n$ and then the sum of series. We know that\\ \b... rac{2^5}{2^4}=2$$ and $$a_n=2^{10}$$.\\ We first find $n$ and then the sum of series. We know that\\ \b
- Question 1 and 2 Exercise 4.2
- KPTBB) Peshawar, Pakistan. =====Question 1===== Find the $15$th term of the arithmetic sequence $2,5,8... an arithmetic sequence is 8 and the 21st is 108. Find the 7th term. GOOD ====Solution==== Since $a_1=8$
- Question 3 and 4 Exercise 4.2
- KPTBB) Peshawar, Pakistan. =====Question 3===== Find the numbers of terms in arithmetic progression $6... . Show that it is an arithmetic progression. Also find its 7th term. ====Solution==== Given that $$a_n=2
- Question 1 Exercise 4.3
- TBB) Peshawar, Pakistan. =====Question 1(i)===== Find indicated term and sum of the indicated number of... 20 terms is -200. GOOD =====Question 1(ii)===== Find indicated term and sum of the indicated number of
- Question 5 & 6 Exercise 4.3
- KPTBB) Peshawar, Pakistan. =====Question 5===== Find four numbers in an arithmetic sequence, whose sum... =-6 \text { and } \\ x_3+x_8+x_{12}&=-11, \text { find } \\ x_3+x_8+x_{22} .\end{align} ====Solution====
- Question 7 & 8 Exercise 4.3
- KPTBB) Peshawar, Pakistan. =====Question 7===== Find: $1+3-5+7+9-11+13+15-$ $17+\ldots$ upto $3 n$ ter... s each one in parenthesis is arithmetic,\\ we can find the sum of $\mathrm{n}$ terms of each, and\\ then
- Question 2 & 3 Exercise 4.4
- ric sequence is $27$ and the fifth term is $243$. Find the first term and common ratio of the sequence. ... nce}\quad a_1=3, r= \pm 3$$ =====Question 3===== Find the seventh term of the geometric sequence that h