Question

If $a,b,c$ are in $A.P$, then show that $3^a,3^b,3^c$ are in $G.P$

Answer 1

a,b,c are in A.P

$\therefore 2b=a+c$

Also $b-a=c-b$_____$\left(1\right)$

$\therefore \frac{3^b}{3^a}=3^{b-a}$ _____$\left(2\right)$

$\therefore \frac{3^c}{3^b}=3^{c-b}$ ______$\left(3\right)$

$\therefore$ from $\left(1\right),\left(2\right),\left(3\right)$

$3^a,3^b,3^c$ are in G.P.