Arithmetic Progression

For each positive integer $\text{k}$, let ${\text{S}}_{\text{k}}$ denote the increasing arithmetic sequence of integers whose first term is $\text{1}$ and whose common difference is $\text{k}$. For example,${\text{ S}}_{\text{3}}$ is the sequence $\text{1, 4, 7, 10 ..............}$. Find the number of values of $\text{k}$ for which ${\text{S}}_{\text{k}}$ contain the term $\text{361}$.

The seventh common term between the series $3+7+11+15+......$ and $1+6+11+16+.......$ is $T$, then $T-100$ equals$?$

A car covers a distance of $65$ km in first hour of its journey, $55$ km in second hour and $90$ km in the last hour. Find the average speed of the car for the whole journey.

A series has $6$ consecutive odd numbers such that the last number of the series is one-third of $429$. Find the arithmetic mean of the series.

Find the arithmetic mean of three numbers such that the first number is $40\%$ more than the second number and also $30\%$ less than the third number. Third number is $50$.

The sum of odd integers from $1$ to $2001$ is

Three numbers are in arithmetic progression. Their sum is $21$ and the product of the first number and the third number is $45.$ Then the product of these three number is

Let $a_n,n\ge 1,$ be an arithmetic progression with first term $2$ and common difference $4 .$ Let $M_n$ be the average of the first $n$ terms. Then the sum $\sum _{n=1}^{10}{M}_n$ is

Suppose the sum of the first $m$ terms of an arithmetic progression is $n$ and the sum of its first $n$ terms is $m$ where $m\ne n$. Then, the sum of the first $(m+n)$ terms of the arithmetic progression is
 

If for an arithmetic progression, $9$ times ninth term is equal to $13$ times thirteenth term, then value of twenty-second term is

If the sum of first $n$ terms of an A.P. be $3n^2-n$ and its common difference is $6$, then its first term is
 

The number of terms of the A.P. $3, 7, 11, 15\dots$ to be taken so that the sum is $406$, is

If the first term of an A.P. is $10$, last term is $50$ and the sum of all the terms is $300$, then the number of terms are

Let the sets $A=\left\{2, 4, \mathrm{6,} 8\dots \right\}$ and $B=\left\{3, 6, 9,12\dots \right\}$ such that $n\left(A\right)=200$ and  $n\left(B\right)=250.$ If $n\left(A\cup B\right)=k$, then $\frac{k}{100}$ is equal to

Which of the following is not an absolute measure of dispersion?

In a race, the first four winners are to be awarded points .Each winner’s points must be 5 more than that of the next position winner. Total sum of the points to be awarded is 50. What will be the points for the third position winner?

Four quantities are such that their arithmetic mean (A.M) is the same as the A.M of the first three quantities. The fourth quantity is:

If ${19}^{th}$ term of a non-zero A.P. is zero, then the value of $\frac{a_{49}}{a_{29}}$ where $a_n$ denotes the $n^{th}$ term of an A.P is:

For how many days, the rainfall was less than the mean rainfall?