In a G.P. the third term is 24, and the sixth term is 192. Find the tenth term.

${ \boxed{ \red{ \bold{3072}}}}$

Step-by-step explanation:

Given,

${ \green{ \sf{ {ar}^{2} = 24}}} \: { \to} \: { \tt{ {eq}^{n} (1)}}$

${ \green{ \sf{ {ar}^{5} = 192}}} \: { \to} \: { \tt{ {eq}^{n} (2)}}$

From Eqⁿ (2),

${ \green{ \sf{ {ar}^{2}. {r}^{3} = 192}}}$

${ \green{ \sf{24. {r}^{3} = 192}}}$

${ \green{ \sf{ {r}^{3} = \frac{192}{24}}}}$

${ \green{ \sf{ {r}^{3} = 8}}}$

${ \green{ \sf{ {r}^{3} = {2}^{3}}}}$

${ \boxed{ \purple{ \sf{r = 2}}}}$

From Eqⁿ (1)

${ \blue{ \sf{ {ar}^{2} = 24}}}$

${ \blue{ \sf{a {(2)}^{2} = 24}}}$

${ \blue{ \sf{4a = 24}}}$

${ \blue{ \sf{a = \frac{24}{4}}}}$

${ \boxed{ \purple{ \sf{a = 6}}}}$

10th term is,

${ \orange{ \sf{ {ar}^{9} }}}$

${ \orange{ \sf{6 {(2)}^{9}}}}$

${ \orange{ \sf{6(512)}}}$

${ \bold{ = }}{ \boxed{ \red{ \bold{3072}}}}$

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In a G.P. the third term is 24, and the sixth term is 192. Find the tenth term.​