Complete the a.p series with given information - class-XI
Description: complete the a.p series with given information | |
Number of Questions: 75 | |
Created by: | |
Tags: sequences and series progressions sequence, progression and series binomial theorem, sequence and series maths arithmetic progressions |
$a$ should be $5$ to make the series $2,a,8,...$ to be in AP
If the solution as $\cos p\theta +\cos q\theta=0$ are in $AP$ then the common difference is
The $n^{th}$ term of the series $3+7+14+24+.....$ is
A line passes through the variable point $A(\lambda +1,2\lambda)$ meets the lines $7x+y-16=0,\ 5x-y-8=0,\ x-5y+8=0$ at $b,c,d$ respectively. Then $AC, AB, AD$ are in
If $T _n$ denotes the nth terms of the series.$ 2+3+6+11+18+..........$ , then $T _50$ is :
If the m+n, n+p, p+n terms of an AP are a, b, c respectively, then m(b-c)+n(c-a)+p(a-b) is
Let $a,b,c$ be in AP and $k\neq 0$ be a real number. WHich of trhe following are correct ?
1.$ka,kb,kc$ are in Ap
2. $k-a,k-b,k-c$ are in AP
3. $\dfrac{a}{k},\dfrac{b}{k},\dfrac{c}{k}$ are in AP
Select the correct answer using the code given below :
Find the next term of the series:
$22, 26, 29, 31,$ ..........
$\displaystyle a^{2}\left ( b+c \right ),b^{2}\left ( c+a \right ),c^{2}\left ( a+b \right )$ provided $\displaystyle \sum ab\neq 0.$ if $a=b=c$ then above series is in:
If the $m^{th}$ term and the $n^th$ term of an AP are respectively $\displaystyle \frac { 1 }{ n } $ and $\displaystyle \frac { 1 }{ m } $, then the $mn^{th}$ term of the AP is
Which one is an example of A.P. property?
Identify the property of A.P. used in the sequence:
In an arithmetic progression the sum of two terms equidistant from the beginning and the end is always _____ to the sum of the first and last terms.
$\dfrac{1}{x},\dfrac{2}{x},\dfrac{3}{x},....$ is a property of
In which property the sum of two terms equidistant from the beginning and the end is always same or equal to the sum of the first and last terms?
How many natural numbers are there between $23$ and $100$ which are exactly divisible by $24$?
The sum of first $10$ terms and $20$ terms of an AP are $120$ and $440$ respectively. What is the first term?
$T _m$ denotes the number of Triangles that can be formed with the vertices of a regular polygon of $m$ sides.If $T _m+ _1-T _m=15$ , then $m$
Which term of A.P. $20, 19\displaystyle\frac{1}{4}, 18\frac{1}{2}$,..... is first negative term?
${ T } _{ m }$ denotes the number of triangles that can be formed with the vertices of a regular polygon of m sides. If ${ { T } _{ m+1 } }-{ { T } _{ m } }=15,$ then $m=$
If $a,b,c$ are distinct and the roots of $\left( b-c \right) { x }^{ 2 }+\left( c-a \right) x+\left( a-b \right) =0$ are equal, then $a,b,c $ are in
Say true or false.
In an $A.P$., sum of terms equidistant from the beginning and end is constant and is equal to the sum of the first and last term.
If $a,b,c$ are in $A.P.$, then the straight lines $ax+by+c=0$ wil always pass through the point ..........
An AP consists of $15$ terms. The three middle most terms is $69$ and the last three terms is $123$. Find the A.P.
If $x,y,z$ are $p^{th},q^{th}$ and $r^{th}$ terms respectively of a $G.P$., then $x^{q-r}\cdot y^{r-p}\cdot z^{p-q}$ is simplified to
If $f _n(x)=\frac{sinx}{cos3x}+\frac{sin3x}{cos3^2x}+\frac{sin3^2x}{cos3^3x}+..........+ \frac{sin3^{n-1}x}{cos3^nx}$ then $f _2$
The largest term to common to the sequences $1,11,21,31,... to 100$ terms and $31,36,41,46, ...to 100$ terms is
If $a^{2},b^{2},c^{2}$ are in $AP$, then which of the following are in $AP$?
If $a,b$ and $c$ are in $A.P.,$ then $\dfrac{(a-c)^{2}}{b^{2}-ac}=$ ?
If $a, b, c$ are in $A.P.$ then $\left|\begin{matrix} x+1 & x+2 & x+a \ x+2 & x+3 & x+b \ x+3 & x+4 & x+c \end{matrix}\right|$
If $x \in R,$ the numbers ${2^{1 + x}} + {2^{1 - x}},b/2,{36^x} + {36^{ - x}}$ form an A.P. , then $b$ may lie in the interval
State the whether given statement is true or false
For a positive integer n,let $S(n)=1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+.....+\dfrac{1}{2^n-1}$. Then prove that $S(100)<100$.
If $9^{th}$ term of an A.P. be zero then the ratio of its $2022^{th}$ and $10^{th}$ term is.......
If the angles $A,B,C$ of a $\triangle ABC$ are in $A.P.$, then:-
If a, b, c are in A.P., then $a ^ { 3 } + c ^ { 3 } - 8 b ^ { 3 }$ is equal to:
If $\dfrac{1}{b-c},\dfrac{1}{c-a},\dfrac{1}{a-b}$ be consecutive terms of an AP then $(b-c)^2,(c-a)^2,(a-b)^2$ will be in ?
If we divide $20$ into four parts which are in A.P such that product of the first and the fourth is to the product of the second and the third is the same as $2$:$3$ then the smallest part is
The mean of a data set consisting of $20$ observations is $40$. If one observation $53$ was wrongly recorded as $33$, then the correct mean will be:
If $log2,log({ 2 }^{ x }-1)and\quad log({ 2 }^{ x }+3)$ are in A.P., then x is equal to :
If $\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in A.P., then $(\frac{1}{a}+\frac{1}{b}-\frac{1}{c})(\frac{1}{b}+\frac{1}{c}-\frac{1}{a})$ is equal to:
Suppose in $\Delta ABC$, ex-radii $r _1,r _2,r _3$ are H.P. then the sides $a,b,c$
If the ratio of sum of n terms of two sequences is (3n+8):(7n+15), then the ratio of their $ 12^{th}$ term is ---------.
Let ${a _1},{a _2},{a _3}.....$ and ${b _1},{b _2},{b _3}......$ be AP such that ${a _1}=25,{b _1}=75$ and ${a _{100}} + {b _{100}} = 100$. Then,
If the roots of palynomial $P ( x ) = x ^ { 3 } - 3 x ^ { 2 } + k x + 4 $ are in $A P ,$ then $\left| k \right| $. Has the value equal to
If the non-zero terms $x , y, z$ are in $AP $ and $\tan ^ { -1 } x, \tan ^ { - 1 } y, \tan ^ { - 1 } x$ are also $AP$ then
If roots of the equation $(a-b)x^{2}+(c-a)x+(b-c)=0, a \neq b \neq c$ are equal, then $a,b,c$ are in
If a, b, c are in AP then $a+\frac{1}{bc}$, $b+\frac{1}{ca}$, $c+\frac{1}{ab}$ are in
Let $a _1, a _2,....a _{10}$ be in AP, and $h _1, h _2,...., h _{10}$ be in HP. If $a _1=h _1=2$ and $a _{10}=h _{10}=3$, then $a _4h _7$ is?
Which term of the sequence $72, 70, 68, 66, ...$ is $40$ ?
If $1,\,{\log _y}x,\,{\log _z}y,\, - \,15{\log _{x}z}$ are in $A.P.$ , then
The series $4,13,22,31,40,......$ is in
a proper option (a), (b), (c) or (d) from given options and write in the box given that so that the statement becomes correct : (All the problems refer to A.P)
${ T } _{ 3 }=8,{ T } _{ 7 }=24,$ then ${ T }$
Select the correct option.
The first term of an $AP$ is $p$ and the common difference is $q$, then its $10^{th}$ term is
Select the correct option.
The value of $x$ for which $2x, (x + 10) $ and $(3x + 2)$ aree the three consecutive terms of an AP, is
$\displaystyle \frac{b+c-a}{a}, \frac{c+a-b}{b}, \frac{a+b-c}{c}$ are in A.P., then $\displaystyle \frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in
Let $S _n$ be the sum of all integers k such that $2^n < k < 2^{n-1}$, for n > 1, Then $9$ divides $S _n$ if and only if
The sum of the three numbers in A.P is $21$ and the product of the first and third number of the sequence is $45$. What are the three numbers?
The sum of $10$ numbers is $100$. The first term is $1$. Find its common difference.
The sum of first $10$ terms and $20$ terms of an AP are $120$ and $440$ respectively. What is the common difference?
If ${ a } _{ 1 },{ a } _{ 2 },{ a } _{ 3 },\dots $ are terms of AP such that ${ a } _{ 1 }+{ a } _{ 5 }+{ a } _{ 10 }+{ a } _{ 15 }+{ a } _{ 20 }+{ a } _{ 24 }=225$, then the sum of first $24$ terms is
$x _{1}, x _{2}, x _{3}, ....$ are in A.P.
If $x _{1} + x _{7} + x _{10} = -6$ and $x _{3} + x _{8} + x _{12} = -11$, then $x _{3} + x _{8} + x _{22} = ?$
If the $n^{th}$ term of an AP be $(2n-1)$, then the sum of its first n terms will be.
If $a,b,c$ are distnct and the roots of $(b-c)x^{2}+(c-a)x+(a-b)=0 $are equal, then $a,b,c$ are in
If the $p^{th}$, $q^{th}$ and $r^{th}$ terms of an A.P. are P, Q, R respectively, then $P(q-r)+Q(r-p)+R(p-q)$ is equal to _________.
If $\sin { \ \alpha },\ \sin ^{ 2 }{ \ \alpha },\ 1,\ \sin ^{ 4 }{ \ \alpha }$ and $\ \sin ^{ 5 }{ \ \alpha }$ are in A.P. where $-\pi <a<\pi$, then $\alpha$ lies in the interval-
The sum of all the natural numbers from $200$ to $600$(both inclusive) which are neither divisible by $8$ nor by $12$ is?
The line joining $A$ $\left( b\cos { \alpha ,\ b\sin { \alpha } } \right)$ and $B$ $\left( a\cos { \beta ,\ a\sin { \beta } } \right)$ is produced to the point $M$ $\left( x,y \right)$, so that $AM$ and $BM$ are in the ration $b:a$. Prove that
$x+y\ \tan { \left( \dfrac { \alpha +\beta }{ 2 } \right) } =0$
Find the sum of the first $15$ terms of the following sequences having $n$th term as
${a} _{n}=3+4n$
Let ${V} _{r}$ denote the sum of the first $r$ terms of an A.P whose first term is $r$ and common difference is $(2r-1)$.Let
${T} _{r}={V} _{r+1}-{V} _{r}-2$ and
${Q} _{r}={T} _{r+1}-{T} _{r}$ $T$ is always
Let $f(x)=3ax^{2}-4bx+c(a,b,c \in R, a \neq 0)$ where $a,b,c$ are in $A.P$. Then the equation $f(x)=0$ has
If $ab + bc + ca =0$ , then the value of $\frac{1}{{{a^2} - bc}} + \frac{1}{{{b^2} - ca}} + \frac{1}{{{c^2} - ab}}$ will be
If $x,y,z$ are in A.P. then the value of the det A where $A=\begin{bmatrix} 4 & 5 & 6 & x \ 5 & 6 & 7 & y \ 6 & 7 & 8 & z \ x & y & z & 0 \end{bmatrix},$ is
If $\displaystyle \frac{b+c-a}{a},\frac{c+a-b}{b},\frac{a+b-c}{c}$ are in A.P.,then $\displaystyle\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in
The sum of all terms of the arithmetic progression having ten terms except for the first tens, is 99, and except for the sixth term, is 89. Find the third term of the progression if the sum of the first and the fifth term is equal to 10.