Question 1 :
Constant is subtracted from each term of an A.P. the resulting sequence is also an ______
Question 2 :
3, 7, 11, 15, 19, ...... are in AP. find 25th term.
Question 5 :
Show that the sequence defined by $a_n = 5n -7$ is an AP. Also, find its common difference.
Question 6 :
The sum of six consecutive numbers is $150$. Find the first number
Question 7 :
If a,b,c are distinct and the roots of (b-c)$x^{2}$ + (c-a) x + (a-b) = 0 are equal ,then a,b,c are in
Question 9 :
The AP whose first term is 10 and commondifference is 3 is
Question 10 :
$\sum\limits_{i = 1}^n {\sum\limits_{j = 1}^i {\sum\limits_{k = 1}^j 1 } } $ is equal to
Question 11 :
If $18, A, B, -3$ are in arithmetic sequence, find the values of $A$ and $B$.
Question 12 :
Find the $21^{st}$ term of an A.P. whose $1^{st}$ term is $8$ and the $15^{th}$ term is $120$.
Question 13 :
If $ a_{n} $ is an A.P and $a_{1}+ a_{4}+ a_{7}+...+a_{16}=147$, then $a_{1}+a_{6}+a_{11}+a_{16}=$
Question 14 :
The sum of all odd integers between $2$ and $50$ divisible by $3$ is
Question 15 :
Given$f(x) = \left[ {\frac{1}{3} + \frac{x}{{66}}} \right]$ then$\sum\limits_{x = 1}^{66} {f(x)} $ is
Question 17 :
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 18 :
A cricketer has to score $4500$ run. Let$a_{n}$ denotes the number of run he scores in the $n^{th}$ match. If $a_{1}=a_{2}=......=a_{10}=150$ and $a_{10},a_{11},a_{12}$,... are in A.P. with common difference -2, then find the total number of matches played by him to score 4500 runs
Question 19 :
If $m$ times the $m^{th}$ term of an A.P. is equal to $n$ times its $n^{th}$ term, find the $(m + n)^{th}$ term of the A.P.
Question 20 :
If $(1 + 3 + 5+...+p) + (1 + 3 + 5+...+q) =(1 + 3 + 5 + ... + r)$ where each set of parentheses contains the sum of consecutive odd integers as shown, the smallest possible value of $p + q + r$, (where $p > 6$) is
Question 24 :
Assertion: There exists no A.P. whose three terms are $\sqrt 3, \sqrt 5$ and $\sqrt 7$.
Reason: If $t_p, t_q$ and $t_r$ are three distinct terms of an A.P., then $\frac {\displaystyle t_r-t_p}{\displaystyle t_q-t_p}$ is a rational number.
Question 25 :
If the sum of first p terms, first q terms and first r terms of an A.P . be a, b and c respectively, then $\dfrac {a}{p}(q-r)+\dfrac {b}{q}(r-p)+\dfrac {c}{r}(p-q) $ is equal to