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

Options

A. `a=b=c`
B. `agebgec`
C. `a+c=b`
D. `ac-b^(2)=0`

Answer

B, D

Explanation

In a AP of `(2n-1)` terms, nth term =a
In a GP of `(2n-1)` terms, nth term =b
In a HP of `(2n-1)` terms, nth term =c
a,b,c will be arithmetic mean, geometric mean, harmonic mean, respectively.
So, `a ge b gec` and `b^(2)=ac`
.