Mathematics - Sequence & Series Question with Solution | TestHub

Let $\beta$ be the inclination of the plane to the horizontal and $u$ be the velocity of projection of the projectile ${\mathrm{R}}_1=\frac{{\mathrm{u}}^2}{\mathrm{g}(1+\sin \beta )}$ and ${\mathrm{R}}_2=\frac{{\mathrm{u}}^2}{\mathrm{g}(1-\sin \beta )}$ $\frac{1}{{\mathrm{R}}_1}+\frac{1}{{\mathrm{R}}_2}=\frac{2\mathrm{g}}{{\mathrm{u}}^2}$ or $\frac{1}{{\mathrm{R}}_1}+\frac{1}{{\mathrm{R}}_2}=\frac{2}{\mathrm{R}}\left[\because \mathrm{R}=\frac{{\mathrm{u}}^2}{\mathrm{g}}\right]$ Therefore, ${\mathrm{R}}_1,\mathrm{R},{\mathrm{R}}_2$ are in H.P.