[tex] > resolucao \\ \\ > progressao \: geometrica \\ \\ \geqslant \: a \: razao \: da \: pg \\ \\ an = a1 \times q {}^{n - 1} \\ 729 = \frac{1}{9} \times q {}^{5 - 1} \\ 729 = \frac{1}{9} \times q {}^{4} \\ \frac{729}{ \frac{1}{9} } = q {}^{4} \\ 729 \times \frac{9}{1} = q {}^{4} \\ 6561 = q {}^{4} \\ 9 {}^{4} = q {}^{4} \\ q = 9 \\ \\ \\ \\ \geqslant produto \: da \: pg \\ \\ \\ pn = a1 {}^{n} \times q {}^{ \frac{n(n - 1)}{2} } \\ pn = ( \frac{1}{9} ) {}^{5} \times 9 {}^{ \frac{5(5 - 1)}{2} } \\ pn = \frac{1}{59049} \times 9 \frac{5.4}{2} \\ pn = \frac{1}{59049} \times 9 {}^{ \frac{20}{2} } \\ pn = \frac{1}{59049} \times 9 {}^{10} \\ pn = \frac{1}{59049} \times 3486784401 \\ pn = \frac{3486784401}{59049} \\ pn = 59049 \\ pn = 3 {}^{10} \\ \\ \\ \\ resposta \: > \: letra \: ( \: b \: ) \\ \\ \\ > > > > > > > [/tex]
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[tex] > resolucao \\ \\ > progressao \: geometrica \\ \\ \geqslant \: a \: razao \: da \: pg \\ \\ an = a1 \times q {}^{n - 1} \\ 729 = \frac{1}{9} \times q {}^{5 - 1} \\ 729 = \frac{1}{9} \times q {}^{4} \\ \frac{729}{ \frac{1}{9} } = q {}^{4} \\ 729 \times \frac{9}{1} = q {}^{4} \\ 6561 = q {}^{4} \\ 9 {}^{4} = q {}^{4} \\ q = 9 \\ \\ \\ \\ \geqslant produto \: da \: pg \\ \\ \\ pn = a1 {}^{n} \times q {}^{ \frac{n(n - 1)}{2} } \\ pn = ( \frac{1}{9} ) {}^{5} \times 9 {}^{ \frac{5(5 - 1)}{2} } \\ pn = \frac{1}{59049} \times 9 \frac{5.4}{2} \\ pn = \frac{1}{59049} \times 9 {}^{ \frac{20}{2} } \\ pn = \frac{1}{59049} \times 9 {}^{10} \\ pn = \frac{1}{59049} \times 3486784401 \\ pn = \frac{3486784401}{59049} \\ pn = 59049 \\ pn = 3 {}^{10} \\ \\ \\ \\ resposta \: > \: letra \: ( \: b \: ) \\ \\ \\ > > > > > > > [/tex]