Question

if a b c are in GP prove that A cube B cube C Q are in a GP

Answer 1

$Let \: a \: b \: and \: c \: be \: in \: GP \: with \: r \: as \: the \: common \: ratio \\ Hence \\ b = \: ar \: and \: c = \: br \: = \: arr \\ Now \: if \: we \: cube \: then \\ {b}^{3} = {ar}^{3} \\ { c}^{3} = {br}^{3} = {ar}^{3} {r}^{3} \\ \\ {a}^{3} \: {b}^{3} \: {c}^{3} \: can \: be \: written \: as \: \\ {a}^{3} \: {a}^{3} {r}^{3} \\ {a}^{3} {r}^{3} {r}^{3} \\ the \: common \: ratio \: is \: {r}^{3}$