[tex] > \: resolucao \\ \\ \geqslant \: progressao \: \: geometrica \\ \\ a1 = \frac{1}{4} \\ an = 32 \\ n = 8 \\ \\ = = = = = = = = = = = = = = = = \\ \\ > \: a \: razao \: da \: pg \\ \\ an = a1 \times q {}^{n - 1} \\ 32 = \frac{1}{4} \times q {}^{8 - 1} \\ 32 = \frac{1}{4} \times q {}^{7} \\ \frac{32}{ \frac{1}{4} } = q {}^{7} \\ 32 \times \frac{4}{1} = q {}^{7} \\ \frac{128}{1} = q {}^{7} \\ 128 = q {}^{7} \\ 2 {}^{7} = q {}^{7} \\ q = 2 \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant [/tex]