If the and terms of an A.P and G.P. are equal and are then prove that...

If the m^{{th}{~}},n^{{th}{~}} and p^{{th}{~}} terms of an A.P and G.P. are equal and are x,y,z then prove that x^{y - z} \cdot y^{z - x} \cdot z^{x - y} = 1: Sequence & Series (Mathematics)

If the

m^{\text{th}\text{~}},n^{\text{th}\text{~}}

and

p^{\text{th}\text{~}}

terms of an A.P and G.P. are equal and are

x,y,z

then prove that

x^{y - z} \cdot y^{z - x} \cdot z^{x - y} = 1