Question

If $a, b, c$ are in A.P., then $7^a, 7^b,$ and $7^c$ are in

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

Answer 1

Answer: (B)

G.P

Answer 2

$a, b , c$ are in A.P.
Let $7^a = x, 7^b = y, 7^c = z$
$\Rightarrow \:\: a \log 7 = \log x, b \log 7= \log y, c \log 7 =\log z$
Since, $a, b, c$ are in A.P.
$\therefore \:\:\: 2b = a + c$
i.e., $2 \frac{\log y}{\log 7}= \frac{\log x}{\log 7}+\frac{\log z}{\log 7}$
$\Rightarrow 2 \log y =\log x+\log z$
$\Rightarrow \log y^{2}=\log x\cdot z \Rightarrow y^{2} =xz$
$\therefore\:\:\: x,y,z$ are in G.P.
$\Rightarrow \:\:\:7^a, 7^b ,7^c$ are in G.P.