If a, b, c are in GP, prove that

To prove: $a^{3}, b^{3}, c^{3}$ are in GP

Given: $a, b, c$ are in GP

Proof: As a, b, c are in GP

$\Rightarrow b^{2}=a c$

Cubing both sides

$\Rightarrow\left(b^{2}\right)^{3}=(a c)^{3}$

$\Rightarrow b^{6}=a^{3} c^{3}$

$\Rightarrow \frac{b^{3}}{a^{3}}=\frac{c^{3}}{b^{3}}=$ common ratio $=r$

From the above equation, we can say that $a^{3}, b^{3}, c^{3}$ are in GP