Question 1 :
The sum of all odd integers between $2$ and $50$ divisible by $3$ is
Question 2 :
<b>Statement 1 : </b>Coefficient of ${ x }^{ 14 }$ in ${ \left( 1+2x+{ 3x }^{ 2 }\cdots +{ 16x }^{ 15 } \right) }^{ 2 }$ is 560<br><br><b>Statement 2 :</b> $\sum _{ r=1 }^{ n }{ r(n-r)\quad =\quad \cfrac { n({ n }^{ 2 }-1) }{ 6 } } $<br><br>
Question 3 :
Which term of the A.P. : 21, 42, 63, 84, .... is 210?<br>
Question 4 :
Four numbers are in arithmetic progression.The sum of first and last term is $8$ and the product of both middle terms is $15$. The least number of the series is.
Question 5 :
If $ \log_e 5 , \log_e ( 5^x - 1) $ and $ \log_e \left( 5^x - \dfrac {11}{5} \right) $ are in $AP,$ then the values of $x$ are :
Question 6 :
Find the second term and $nth$ term of an AP whose $6th$ term is $12$ and $8th$ term is $22.$
Question 7 :
The first and last terms of an A.P of n terms is 1, 31 respectively. The ratio of $8^{th}$ term and $(n-2)^{th}$ term is 5:9, the value of n is:<br>
Question 8 :
If the sum of 16 terms of an arithmetic progression is 1624 and the first term is 500 times the common difference, then find the common difference.
Question 10 :
If the $p^{th},q^{th},r^{th}$ and $s^{th}$ terms of an A.P. are in G.P,. then $ p-q, q-r, r-s $ are in
Question 11 :
What is the sum of all positive integers up to $1000$, which are divisible by $5$ and are not divisible by $2$?
Question 12 :
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 13 :
The difference any two consecutive interior angles of a polygon is $5^{\circ}$.If the smallest angle is $120^{\circ}$, find the number of the sides of the polygon.
Question 14 :
If 9 times the $9^{th}$ term of an AP is equal to 13 times the $13^{th}$ term, then the $22^{nd}$ term of the AP is: 
Question 15 :
If $18, A, B, -3$ are in arithmetic sequence, find the values of $A$ and $B$.
Question 16 :
Given$f(x) = \left[ {\frac{1}{3} + \frac{x}{{66}}} \right]$ then$\sum\limits_{x = 1}^{66} {f(x)} $ is
Question 17 :
If $7th$ and $13th$ terms of an $A.P$. Be $34$ and $64$, respectively, then its $18th$ terms is:
Question 18 :
The sum up to $9$ terms of the series $\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{6}+ ...$ is<br/>
Question 19 :
$\displaystyle \frac{b+c-a}{a}, \frac{c+a-b}{b}, \frac{a+b-c}{c}$ are in A.P., then $\displaystyle \frac{1}{a}, \frac{1}{b}, \frac{1}{c}$are in
Question 20 :
If the sum of a certain number of terms starting from first of an AP $25, 22, 19,..$is $116.$ Find the last term.
Question 21 :
If the first four terms of an arithmetic sequence are $a, 2a, b$ and $a - 6 - b$ for some numbers $"a"$ and $"b"$, find the value of the $100^{th}$ terms
Question 22 :
<p>If first, second and last terms of an A.P. are a,b and c<br>respectively. Then the number of terms =</p>
Question 23 :
If $log_{10} a, log_{10}, log_{10} c$ are in A.P., then $a, b, c$ must be in<br>
Question 24 :
What is the sum of the first $n$ terms if the first term is $2$, the common difference is $5$ and the $n^{th}$ term is $122$ in an arithmetic series?<br/>
Question 25 :
What is the tenth term of the arithmetic sequence whose first term is $x$ and whose third term is $x + 6a$?
Question 26 :
What is the fifth term of the arithmetic sequence $2,$ _, $8$, _, _, ...?
Question 27 :
An A.P. consists of $13$ terms of which $2^{nd}$ terms is $10$ and the last term is $120$. Find the $9^{th}$ term.
Question 28 :
The sum of the series $\displaystyle \left(4-\frac{1}{n}\right)+\left(4-\frac{2}{n}\right)+\left(4-\frac{3}{n}\right)+\cdots$ upto $n$ terms is
Question 29 :
If the third term of an $A.P.$is $7$and its $7^{th}$term is $2$more than three times of its $3^{rd}$term, then sum of its first $20$terms is-
Question 30 :
What is the sum of the series $3 - 5 - 13... -229?$<br/>