If first and `(2n-1)^(th)` terms of A.P., G.P. and H.P. are equal and their nth terms are a,b,c respectively, then

Options

A. a=b=c
B. `a ge be ge c`
C. `a+b =c`
D. `ac- b^2 =0 `

Answer

B, D

Explanation

Let x be the first term and y be the (2n-1)th term of A.P., G.P. and H.P. whose nth terms are a,b,c, respectively.
According to the property of A.P., G.P. and H.P.,
xa,y are in A.P.
x,b,y are in G.P.
x,c,y are in H.P.
Using this information, we get
`a=(x+y)/2=A.M.`
`b=sqrt(xy)=G.M.`
and `c=(2xy)/(x+y)`=H.M.
We know that A.M.,G.M. and H.M. are in G.P..
`thereforeb^(2)=ac`
Also, A.M.`ge`G.M.`ge`H.M.
`rArragebgec`