Introduction to Arithmetic Progressions

Define arithmetic progression.

The sum of first $n$ terms of an AP is $210$ and sum of its $(n-1)$ terms is $171$. If the first term is $3$ then, write the AP.

If the roots of $x^3-3p{x}^2+qx-r$ are in A.P, then

Which of the following progression is an A.P.?

An Arithmetic Progression can be determined if its one term and common difference are known to us.

Can we determine an Arithmetic Progression whose any two terms with their positions are known?

Identify the infinite arithmetic progression from the following

Identify the infinite arithmetic progression from the following

Define infinite arithmetic progression

The fourth term of the A.P., $\frac{1}{p},\frac{1-p}{p},\frac{1-2p}{p},....$ is

The ${\left(n – 1\right)}^{\mathrm{th}}$ term of an A.P. is given by $7,12,17, 22,\dots$ is

The fourth term of the A.P., $\frac{1}{p},\frac{1-p}{p},\frac{1-2p}{p},....$ is

For the A.P. $\frac{1}{4}, \frac{-1}{4}, \frac{-3}{4}, \frac{-5}{4}, .....$, the $7^{th}$ term is

The seventh term of an Arithmetic progression is four times its second term and the twelfth term is $2$ more than three times of its fourth term. Find the common difference.

The sequence $\sqrt{3}, \sqrt{6}, \sqrt{9}, \sqrt{12},\dots ..$. form an Arithmetic Progression.

The next two terms of an A.P. $4, 9, 14,.......$

If the $n^{\mathrm{th}}$ term of an arithmetic progression $a_n=24-3n$, then its $2$^nd term is:

There are five terms in an Arithmetic Progression. The sum of these terms is $55,$ and the fourth term is five more than the sum of the first two terms. Find the common difference.

In an arithmetic progression, if $a_n=2n+1,$ then the common difference of the given progression is

Find second and third term of an A.P. whose first term is $-2$ and common difference is $-2$.