Question

If a,b,c are in AP that $\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are

Answer 1

Given $a,b,c$ are in A.P

i.e $2b=a+c$ .. (i)

Three numbers (p,q,r) are sold to be in

Harmone progression if $\frac{2}{q}=\frac{1}{p}+\frac{1}{r}$

Here for $\frac{1}{a},\frac{1}{b},\frac{1}{c}$ $\frac{2}{\left(\frac{1}{a}\right)}=\frac{1}{\left(\frac{1}{b}\right)}+\frac{1}{\left(\frac{1}{c}\right)}$

$\Rightarrow 2a=b+c$

from (1)

$\therefore \frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in Harmonic progression