For $n \in N$,what is the value of $1+4+7+\cdots+(3n-2)$?

Given that $n$ $A$.$M$.'s are inserted between two sets of numbers $a, 2b$ and $2a, b$,where $a, b \in R$. Suppose further that the $m^{th}$ mean between these sets of numbers is the same,then the ratio $a:b$ equals

The sum of all natural numbers between $1$ and $100$ which are multiples of $3$ is

Consider an $A$.$P$.: $a_1, a_2, \dots, a_n$, with $a_1 > 0$. If $a_2 - a_1 = -\frac{3}{4}$, $a_n = \frac{1}{4} a_1$, and $\sum_{i=1}^n a_i = \frac{525}{2}$, then $\sum_{i=1}^{17} a_i$ is equal to:

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

Let $a_1, a_2, a_3, \ldots$ be terms of an $A.P.$ If $\frac{a_1 + a_2 + \ldots + a_p}{a_1 + a_2 + \ldots + a_q} = \frac{p^2}{q^2}$ for $p \ne q$,then $\frac{a_6}{a_{21}}$ equals: