if the mth,nth and pth terms of an AP and GP are equal and are x,y,z respectively,prove that

Question

if the mth,nth and pth terms of an AP and GP  are equal and are x,y,z respectively,prove that

wwe123 · Answer

prove that 
$$x ^{y-z}.y ^{z-x}.z ^{x-y}=1$$

experimentx · Answer

define each of them first 
x = a + (m-1)d <-- for ap,
   = a r^(m-1) <--- for gp

experimentx · Answer

woops!
x = a + (m-1)d <-- for ap,
   = b r^(m-1) <--- for gp

wwe123 · Answer

plz explain more

experimentx · Answer

i don't know at the moment, but i would make full use of info given towards the problem.

wwe123 · Answer

plz solve the question

experimentx · Answer

okay, write the denominators are the Geometric terms and the powers are the Arithemetic terms!! the power cancel up to give zero ... hence you get RHS

experimentx · Answer

sorry ... *write the bases  as Geometric terms 
and exponent as Arithmetic terms

wwe123 · Answer

just show it...

experimentx · Answer

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do the rest for others and multiply it.