The ${19}^{th}$ term of an $AP$ is equal to $3$ times its $6^{th}$ term. If its $9^{th}$ term is $19$, find the $AP$.

If the $p^{th}$term of an $AP$ is  $q$and its $q^{th}$ term is $p$ then show that its $(p + q{)}^{th}$term is zero.

The first and last terms of an $AP$ are $a$ and $l$ respectively. Show that the sum of the $n^{th}$ term from the beginning and the $n^{th}$ term from the end is$( a + l )$.

How many two-digit numbers are divisible by $6$?

How many two-digits numbers are divisible by $3$?

How many three-digit numbers are divisible by $9$?

How many numbers are there between $101$and $999$, which are divisible by both $2$ and $5$?

In a flower bed, there are $43$ rose plants in the first row, $41$ in second, $39$ in the third, and so on. There are $11$ rose plants in the last row. How many rows are there in the flower bed?

A sum of $₹2800$ is to be used to award four prizes. If each prize after the first is $₹200$ less than the preceding prize, find the value of each of the prizes