If `a, b, c` are in AP or GP or HP, then `(a-b)/(b-c)` is equal to

Options

A. `(b)/(a)" or "1" or "(b)/(c)`
B. `(c)/(a)" or "(c)/(b)" or "1`
C. `1" or "(a)/(b)" or "(a)/(c)`
D. `1" or "(a)/(b)" or "(c)/(a)`

Answer

C

Explanation

From equestion,
`a,b,cinA.P.impliesa-b=b-cimplies(a-b)/(b-c)=1`
`a,b,cinG.P.implies(a)/(b)=(b)/(c)=(a-b)/(b-c)`
`a,b,cinH.P.impliesb=(2ac)/(a+c)impliesab+bc=2ac`
`impliesab-ac=ac-bc`
`implies(a-b)/(b-c)=(a)/(c)`