If the sixth term of a $H.P.$ is $\frac{1}{61}$ and its tenth term is $\frac{1}{105},$ then the first term of that $H.P.$ is

If the roots of the equation $16x^3 - 44x^2 + 36x - 9 = 0$ are in harmonic progression,then its greatest root is

If $a, b, c$ are in $H.P.$,then

If there are $n$ harmonic means between $1$ and $\frac{1}{31}$ and the ratio of the $7^{th}$ and $(n - 1)^{th}$ harmonic means is $9:5$,then the value of $n$ is:

If for the series $a_1, a_2, a_3, \ldots$, the expression $a_r - a_{r+1}$ bears a constant ratio with $a_r a_{r+1}$, then $a_1, a_2, a_3, \ldots$ are in:

If $x_1, x_3$ are the roots of $A x^2 - 4 x + 1 = 0$ and $x_2, x_4$ are the roots of $B x^2 - 6 x + 1 = 0$ such that $x_1, x_2, x_3, x_4$ are in harmonic progression,then $\frac{B+A}{B-A} = $