Find the $20^{th}$ term of the $A.P.$ $-40, -15, 10, \ldots$

The first term of an $AP$ is $-5$ and the last term is $45$. If the sum of the terms of the $AP$ is $120$,then find the number of terms and the common difference.

Find the number of terms of the finite $A.P.$ $-1, -\frac{5}{6}, -\frac{2}{3}, \ldots, \frac{10}{3}$.

Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $1.4, 2.3, 3.2, 4.1, \dots$

$Rs. 280$ is to be distributed among four prizes. If the prize amount in each successive prize reduces by $Rs. 20$,find the amounts paid in those prizes.

For a given $A.P.$,the common difference is $5$ and its $15^{th}$ term is $72$. Find the first term of the $A.P.$ and its $50^{th}$ term.