The radius of the first Bohr orbit is $r$. What is the radius of the $2^{nd}$ Bohr orbit?

Assertion $(A)$: The magnetic moment $(\mu)$ of an electron revolving around the nucleus decreases with increasing principal quantum number $(n)$.
Reason $(R)$: Magnetic moment of the revolving electron,$\mu \propto n$.

If $m$ is the mass of an electron,$v$ is its velocity,$r$ is the radius of a stationary circular orbit around a nucleus with charge $Ze$,then from Bohr's first postulate,the kinetic energy of the electron is (where $K = 1 / 4 \pi \epsilon_0$):

The radius of the first (lowest) orbit of the hydrogen atom is $a_0$. The radius of the second (next higher) orbit will be (in $a_0$)

For a certain hypothetical one-electron atom,the wavelength (in $\mathring{A}$) for the spectral lines for transition from $n = p$ to $n = 1$ is given by $\lambda = \frac{1500p^2}{p^2 - 1}$ (where $p > 1$). The ionization potential of this element must be .....$V$ (Take $hc = 12420\ eV\cdot\mathring{A}$).

If the difference between the $(n+1)^{\text{th}}$ Bohr radius and the $n^{\text{th}}$ Bohr radius is equal to the $(n-1)^{\text{th}}$ Bohr radius,then find the value of $n$.