The $4$th term of an $A.P.$ is equal to $3$ times the first term and the seventh term exceeds twice the third term by $1$. Find the first term and the common difference.

The sum of the series $3.6 + 4.7 + 5.8 + \dots$ up to $(n - 2)$ terms is:

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

Let $x, y, z$ be positive real numbers such that $x + y + z = 12$ and $x^3y^4z^5 = (0.1)(600)^3$. Then $x^3 + y^3 + z^3$ is equal to

If $f(x)$ is a function satisfying $f(x + y) = f(x)f(y)$ for all $x, y \in N$ such that $f(1) = 3$ and $\sum_{x = 1}^n f(x) = 120$,then the value of $n$ is

For a series $S = 1 - 2 + 3 - 4 + \dots$ up to $n$ terms,
Statement $-1$: The sum of the series is always dependent on the value of $n$,i.e.,whether it is even or odd.
Statement $-2$: The sum of the series is $-\frac{n}{2}$ when $n$ is any even integer.