Question

what is the nth term of h p

Answer 1

$$\begin{gathered} \mathrm{The}{n}^{th}\mathrm{term}\mathrm{of}\mathrm{H}.\mathrm{P}\mathrm{is}\mathrm{the}\mathrm{reciprocal}\mathrm{of}\mathrm{the}{n}^{th}\mathrm{term}\mathrm{of}\mathrm{the}\mathrm{corresponding}\mathrm{A}.\mathrm{P} \\ \mathrm{Let}a,a+d,a+2d,..........\mathrm{are}\mathrm{in}\mathrm{A}.\mathrm{P} \\ \mathrm{Then},\frac{1}{a},\frac{1}{a+d},\frac{1}{a+2d},.............\mathrm{are}\mathrm{in}\mathrm{H}.\mathrm{P} \\ \mathrm{But}\mathit{}{n}^{\mathit{t}\mathit{h}}\mathit{}\mathrm{term}\mathrm{of}\mathrm{A}.\mathrm{P}=\mathit{}a\mathit{}\mathit{+}\mathit{}\left(\mathit{n}\mathit{}\mathit{-}\mathit{}\mathit{1}\right)\mathit{}d \\ \mathrm{Therefore}\mathit{,}\mathit{}{n}^{\mathit{t}\mathit{h}}\mathrm{term}\mathrm{of}\mathrm{H}.\mathrm{P}=\mathit{}\frac{1}{a+\left(n-1\right)d} \end{gathered}$$