Question

If a, b, c are in H.P then $4^{-a},4^{-b},4^{-c}$ are in

• A. A.P
• B. G.P
• C. H.P
• D. none of these

Answer 1

The correct option is D none of these

Solution : $4^{-a},4^{-b},4^{-c}are$

$\frac{1}{4^a},\frac{1}{4^b},\frac{1}{4^c}$

as clear not in A.P,H.P

$\frac{1}{4^a},\frac{1}{\frac{2ac}{4^{a+c}}},\frac{1}{4^c}$

${\left(\frac{1}{\frac{2ac}{4^{a+c}}}\right)}^2=\frac{1}{\frac{4ac}{4^{a+c}}}$

$\frac{1}{4^a}.\frac{1}{4^c}=\frac{1}{4^{a+c}}$

$4^{-a},4^{-b},4^{-c}$ are also not in G.P.