$A$ man starts repaying a loan with a first installment of $Rs. 100$. If he increases the installment by $Rs. 5$ every month,what amount will he pay in the $30^{th}$ installment?

The sum of all those terms of the arithmetic progression $3, 8, 13, \ldots, 373$ which are not divisible by $3$ is equal to $.......$.

If the roots of the equation $x^3+3px^2+3qx-8=0$ are in an arithmetic progression,then $2p^3-3pq=$

Write the first three terms in each of the following sequences defined by the following:
$a_{n} = 2n + 5$

If the sum of first $n$ terms of an $A.P.$ is equal to the sum of its first $m$ terms,$(m \ne n)$,then the sum of its first $(m + n)$ terms will be

Let $s_1, s_2, s_3, \ldots, s_{10}$ be the sum of the first $12$ terms of $10$ arithmetic progressions whose first terms are $1, 2, 3, \ldots, 10$ and whose common differences are $1, 3, 5, \ldots, 19$ respectively. Then $\sum_{i=1}^{10} s_i$ is equal to