If the average of the first $n$ numbers in the sequence $148, 146, 144, \ldots$ is $125$,then $n$ is equal to

Let $A = \{1, a_{1}, a_{2}, \ldots, a_{18}, 77\}$ be a set of integers with $1 < a_{1} < a_{2} < \ldots < a_{18} < 77$. Let the set $A + A = \{x + y : x, y \in A\}$ contain exactly $39$ elements. Then,the value of $a_{1} + a_{2} + \ldots + a_{18}$ is equal to:

Write the first five terms of the sequence whose $n^{th}$ term is $a_{n} = \frac{2n - 3}{6}$.

Find the maximum sum of the series $20 + 19\frac{1}{3} + 18\frac{2}{3} + 18 + .....$

If the sum of three numbers in an arithmetic progression is $33$ and their product is $792$,what is the smallest number among them?

If the sides of a right-angled triangle are in an arithmetic progression,then they are in the ratio of.........