Question 1 :
<span>Let $r$ be the number of identical terms in the two A.P's. Form the sequence of identical terms, it will be an A.P, then the ${r}^{th}$ term of this A.P make ${t}_{r}\le$ the smaller of the last term of the two A.P's. </span>The number of terms common to two A.P's $3,7,11,....,407$ and $2,9,16,...,709,$ is 
Question 2 :
The $7^{th}$ term of an AP is $-4$ and its $13^{th}$ term is $-16$, find the AP?
Question 3 :
If $p^{th}$ term of an A.P is $q$ and $q^{th}$ term is $p$, then $n^{th}$ term is
Question 4 :
The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is
Question 5 :
The sum of three number in A.P is $12$ and the sum of their cubes is $288$. Find the numbers. 
Question 6 :
The $4^{th}$ term from the end of the A.P.  $-11, -8, -5, ...., 49$ is
Question 7 :
If the $p^{th}, q^{th}$ and $r^{th}$ term of an arithmetic sequence <span>are a, b and c respectively, then the value of <br/>$[a (q r) + b(r p) + c (p q)] =.$</span><br/>
Question 8 :
<span>How many $2$ - digit positive integers are divisible by $4$ or $9$?</span>
Question 9 :
If the sum of three numbers in AP is 12 and the sum of their cubes is 288, then the numbers are
Question 10 :
If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, then its 18th term will be
Question 11 :
If the $ n $ -th term of an arithmetic progression $ a_{n}=24-3 n, $ then its $ 2^{\text {nd }} $ term is
Question 12 :
Example 3. in the following ${ AP }_{ S }$ find teh ,missing terms in the boxes :
Question 13 :
If the lengths of sides of right angled triangle are in A.P then the sines of the acute angles are <br>
Question 14 :
If $a^2,\, b^2,\, c^2$ are in arithmetic progression, then the terms $\dfrac{1}{(a + b)},$ $\dfrac{1}{(c + a)}, \dfrac{1}{(b + c)}$ will form
Question 15 :
Let $a_1, a_2,......a_{50}$ are non constant terms of an A.P. and sum of n terms is given by $S_n=50n+(n)(n-7)\dfrac{A}{2}$, then ordered pair $(d, a_{50})$ is?(where d is the common difference)
Question 16 :
$p^{th}$ term of the series <br/>$\displaystyle \left ( 3-\frac{1}{n} \right )+\left ( 3-\frac{2}{n} \right )+\left ( 3-\frac{3}{n} \right ).......$ will be <br/>
Question 17 :
Choose the correct answer from the given four options in the following questions:<br/>The 21st term of the A.P. whose first two terms are -3 and 4 is
Question 18 :
What is the 20th term of the A.P. 13, 26, 39,....?<br>
Question 19 :
lf the sum to ${n}$ terms of an AP is $\displaystyle \frac{4n^{2}-3n}{4}$ then the $n^{th}$ term of the AP is equal to<br/>
Question 20 :
If the 2nd term of an A.P. is 13 and 5th term is 25, what is the 7th term?
Question 21 :
The ${ 10 }^{ th }$ term of the series $1+5+13+29+...$ is
Question 22 :
Which term of the A.P. $21,42,63,84 , \ldots \ldots . .$ is $210.$
Question 23 :
The sum of n terms of an AP is $2n^{2}+n$. Then 8th term of the A.P is
Question 24 :
Let $T_r$ be the $r$th term of an AP for $r=1, 2...$. If for some positive integers $m$ and $n$ we have $T_m= \dfrac1n$ and $T_n=\dfrac1m$, then $T_{mn} =$
Question 25 :
Let $S_n$ denote the sum of the first n terms of an A.P. If $S_4=16$ and $S_6=-48$, then $S_{10}$ is equal to?
Question 27 :
If ${ a }_{ 1 },{ a }_{ 2 },...{ a }_{ n }$ are in A.P with ${ a }_{ 1 }+{ a }_{ 7 }+{ a }_{ 16 }=40$. Then the value of ${ a }_{ 1 }+{ a }_{ 2 }+......{ a }_{ 15 }$ is
Question 28 :
Which term of the A.P $101, 97, ......$ is its first negative term?
Question 29 :
iF $p ^ { t h }$, $q ^ { t h }$ and $r ^ { t h }$ terms of an A.P are $a, b, c$ then $a ( q - r ) + b ( r - p ) + c ( p - q ) =$
Question 30 :
The sum of $n$ terms of two arithmetic progressions are in ratio $( 3n + 8) : (7n + 15).$ Find the ratio of their $(i) 12th$ terms $(ii) 15th$ terms.
Question 31 :
In the series $20, 18, 16,......... , -2$ is the term 
Question 32 :
Find $n$ if the coefficient of $5^{th}, 6^{th}$ & $7^{th}$ terms in the expansion of $(1+x)^{n}$ are in $A.P.$
Question 33 :
If the 5th term and the 14th term of an AP are 35 and <span>8 respectively, then find the 20th term of the AP.</span>
Question 34 :
 In the sequence ,the first term is $4$ and each term after the first is $7$ more than the previous term. What is the $12^{th}$ term of the sequence? 
Question 36 :
In a given AP is pth termi is q and the qth term is p then its nth term is
Question 37 :
In an A.P., if a = 1, $a_n = 20$ and $s_n = 399$ then n is
Question 38 :
If ${ x }_{ 1 },{ x }_{ 2 },{ x }_{ 3 },....{ x }_{ 4001 }$ are in AP such that $\cfrac { 1 }{ { x }_{ 1 }{ x }_{ 2 } } +\cfrac { 1 }{ { x }_{ 2 }{ x }_{ 3 } } +...+\cfrac { 1 }{ { x }_{ 4000 }{ x }_{ 4001 } } =10$ and ${ x }_{ 2 }+{ x }_{ 4000 }=50\quad $ then $\left| { x }_{ 1 }-{ x }_{ 4001 } \right| =$
Question 39 :
<span>Consider a sequence whose sum to $n$ terms is given by the quadratic function ${S}_{n}=3{n}^{2}+5n$ </span>The nature of the given series is
Question 40 :
$y, 2y + 7, y + 6, ... $<br/>In the increasing sequence above, the first term is $y$ and the difference between any two consecutive terms is $3$. What is the value of the fourth term in the sequence? <br/>
