Question

please answer this question⬆️⬆️​

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Three\:G.M\:are: -8,-16,-32}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\underline { \underline \bold{Given : }} \\ \implies \text{First \: term = - 4} \\ \\ \implies \text{Fifth \: term = - 64} \\ \\ \underline { \underline \bold{To \: Find : }} \\ \implies \text{3 \: g.m \: between \: - 4 \: and \: - 64 = ?}$

• According to given question :

$\text{Let \: three \: terms \: be : } \\ \implies a_{1},a_{2} \: and \: a_{3} \\ \\ \bold{For \: finding \: 3 \: G.M} \\ \implies a_{5} = - 64 \\ \\ \implies a {r}^{4} = - 64 \\ \\ \implies - 4 \times {r}^{4} = - 64 \\ \\ \implies {r}^{4} = \frac{ \cancel{- 64}}{ \cancel{ - 4}} \\ \\ \implies {r}^{4} = 16 \\ \\ \implies r = \sqrt[4]{16} \\ \\ \implies r = 2 \\ \\ \text{Second \: term :} \\ \implies a_{1} = {ar}^{} \\ \\ \implies a_{1} = - 4 \times 2 \\ \\ \implies a_{1} = - 8 \\ \\ \text{Third \: term : } \\ \implies a_{2} = {ar}^{2} \\ \\ \implies a_{2} = - 4 \times {2}^{2} \\ \\ \implies a_{2} = - 16 \\ \\ \text{Forth\: term : } \\ \implies a_{3} = {ar}^{3} \\ \\ \implies a_{3} = - 4 \times {2}^{3} \\ \\ \implies a_{3} = - 4 \times 8 \\ \\ \implies a_{3} = - 32$