Let $a_1, a_2, a_3, \ldots$ be in harmonic progression with $a_1 = 5$ and $a_{20} = 25$. The least positive integer $n$ for which $a_n < 0$ is

$A$ boy goes from his home to school at a speed of $x \text{ km/hr}$ and returns at a speed of $y \text{ km/hr}$. What is the average speed of the boy?

If for the harmonic progression,$t_{7} = \frac{1}{10}$ and $t_{12} = \frac{1}{25}$,then $t_{20} =$

The harmonic mean of the numbers $2, 3, 4$ is:

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of a harmonic progression are $u$,$v$,and $w$ respectively,then the value of $(q - r)vw + (r - p)wu + (p - q)uv$ is equal to:

Let $f(x) = x + 1/2$. Then, the number of real values of $x$ for which the three unequal terms $f(x), f(2x), f(4x)$ are in $HP$ is