Form an AP by inserting $6$ terms between $-4$ and $10$.

Form an AP by inserting $5$ terms between $11$ and $-7$.

If in an arithmetic progression the mean of $p^{\mathrm{th}}$ and $q^{\mathrm{th}}$ term is equal to mean of $r^{\mathrm{th}}$ and $s^{\mathrm{th}}$ term then prove that $p+q=r+s$.

$n$ terms lie between $7$ and $49$ in an AP. If ratio of the third term and the $n^{\mathrm{th}}$ term is $4:5$, then find the value of $n$.

Is the $n^{\mathrm{th}}$ term of a progression is equal to the difference between sum of the first $n$ terms $\left(S_n\right)$ and sum of the first $(n-1)$ terms, $\left(S_{n-1}\right)$?

If the sum of the first n terms of an arithmetic progression is ${\mathrm{S}}_n=4n-n^2$, then can you find the value of the first term? Is this ${\mathrm{S}}_1$? What is the sum of first two terms of this arithmetic progression? What is the second term? In this way find the third the fourth, the fifteenth and the $n^{\mathrm{th}}$ terms.

Find the sum of the following Arithmetic Progression:

$9, 12, 15, ......$ up to $16$ terms.

Find the sum of the following Arithmetic Progression:

$8, 3, -2, ......$ up to $22$ terms.

Find the sum of the following Arithmetic Progression:

$0.6, 1.7, 2.8, ......$ up to $100$ terms.