Introduction to Arithmetic Progressions

What is an AP?

What is A.P?

If the $n$th term of an Arithmetic Progression (A.P.) is $(n+3)$ , then the first three terms of the A.P are:

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

If $a, b, c$ are in A.P then $b=$

Give many examples of arithmetic progression.

Find the common difference of the AP :
$\frac{1}{\mathrm{p}}, \frac{1-\mathrm{p}}{\mathrm{p}}, \frac{1-2\mathrm{p}}{\mathrm{p}} \dots$

What is the actual different between $n$ and $a_n$ in arithemetic progression?

If $a, A, b$ are three consecutive terms of an $A.P.$, then prove that $4\left(a-A\right)\left(A-b\right)={\left(b-a\right)}^2$.

What is mean of AP?

If the $n$th term of an A.P. is given by $a_n=\frac{4n+1}{2}$, then find the common difference

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

If the numbers $\left(2n-1\right), \left(3n+2\right)$ and $\left(6n-1\right)$ are in A.P., find $n$ and hence find these numbers.

Show that the sequence defined by $a_n=4n+5$ is an A.P.  also , find the common difference.

If $p,q$ and $r$ in $A.P$ , then prove that $\left(p+2q-r\right)\left(2q+r-p\right)\left(r+p-q\right)=4pqr$.

Identify the infinite arithmetic progression from the following

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