If the first and (2 n-1) th term of an AP, GP and HP are equal and their n th terms are a, b and c respectively, then 

$$\begin{gathered} \text{ In a AP of }(2\mathrm{n}-1)\text{ terms, }\mathrm{n}\text{th term }=\mathrm{a} \\ \text{ In a GP of }(2\mathrm{n}-1)\text{ terms, }\mathrm{n}\text{th term }=\mathrm{b} \\ \text{ In a HP of }(2\mathrm{n}-1)\text{ terms, }\mathrm{n}\text{th term }=\mathrm{c} \end{gathered}$$
a, b, c will be arithmetic mean, geometric mean, harmonic mean, respectively.
So, $\mathrm{a}\ge \mathrm{b}\ge \mathrm{c}\text{ and }{\mathrm{b}}^2=\mathrm{ac}$