Question 1 :
If k + 2, k, 3k - 2 are three consecutive terms of A.P., then k = .................

Question 2 :
What is the common difference of the new arithmetic progression formed after $4$ is divided from each of the term of the arithmetic progression $20, 28, 36, 44, ...$

Question 3 :
If $a, b, c$ are in A.P. $b - a, c - b$ and $a$ in G.P., then $a:b:c$ is

Question 4 :
In an Arithmetic sequence, $S_{n}$ represents the sum to $n$ terms, what is $S_{n} - S_{n - 1}$?

Question 6 :
The sum of an A.P. whose first term is a, second term is b and the last term is c is equal to $\dfrac{(a+c)(b+c+2a)}{2(b-a)}$.

Question 7 :
Four different integers form an increasing AP. One of these numbers is equal to sum of the squares of the first three numbers, then the common difference of the four numbers is

Question 9 :
Find the number of common terms in the following sequences (each of which is an A.P) which are less than $10,000$.<br>$S_1: 37, 103, 169, \cdots $<br>$S_2: 17, 82, 147, \cdots$

Question 10 :
For the A.P. if $a = 7$ and $d = 2.5 ,$ then $t _ { 12 } = ?$

Question 11 :
The sum of the first three terms of an A.P. is $9$ and the sum of their square is $35$. The sum to first $n$ terms of the series can be

Question 12 :
In an AP,<br/>Given $l = 28, S = 144$&#160; and there are total $9$ terms. Find $a$.

Question 13 :
If a body starts with a velocity $\displaystyle&#160;u $ in a straight line with uniform acceleration f and covers a distance s in time t seconds, and $\displaystyle&#160;s_{t}$ denotes the distance covered by it in the $t$ &#160;seconds, then $\displaystyle&#160;s_{2}, s_{4}, s_{6}$ are in&#160;&#160;

Question 14 :
Let $x_1, x_2, ....., x_n$ be in an AP. If $x_1 + x_4 + x_9 + x_{11} + x_{20} + x_{22} + x_{27} + x_{30} = 272$, then $x_1 + x_2+ x_3 + .... + x_{30}$ is equal to

Question 15 :
The series of natural numbers is divided into groups $(1), (2,3,4), (3,4,5,6,7), (4,5,6,7,8,9,10), ...$ Find the sum of the numbers in nth group.

Question 16 :
If $18, A, B, -3$ are in arithmetic sequence, find the values of $A$ and $B$.

Question 17 :
What is the sum of the series $3 - 5 - 13... -229?$<br/>

Question 18 :
From an $A.P.$first and last term is $13$and $216$respectively. Common difference is $7$. Find the sum of all terms.

Question 19 :
If $a_1, a_2, a_3$,.... are in A.P. such that $a_1+ a_5 + a_{10} + a_{15} + a_{20} + a_{24} =$ 225, then $a_1+ a_2 + a_3+...+a_{23} + a_{24} =$

Question 20 :
The angles of a triangle are in $\displaystyle AP$ and the greatest angle is double the least. The largest angles measures.

Question 22 :
If the product of the first four consecutive terms of a G.P is $256$ and if the commonratio is $4$ and the first term is positive, then its $3^{rd}$ term is<br>

Question 23 :
Assertion: Statement-1 If $a_{1},a_{2},a_{3},..........,a_{24}$ are In A. P. such that $a_{1}+a_{5}+a_{10}+a_{15}+a_{20}+a_{24}=225$ then $a_{1}+a_{2}+a_{3}+......+a_{23}+a_{24}=900$ because Reason: Statement-2 In any A.P. sum of the terms equidistant from begining and end is constant and is equal to<br><br>the sum of the first and the last term,

Question 24 :
All the term of an A. P. are natural numbers and the sum of the first $20$ terms is greaterthan $1072$ and less than $1162$. If the sixth term is $32$ then-