[tex] > resolucao \\ \\ \geqslant progressao \: geometrica \\ \\ \geqslant \: numero \: de \: termos \: da \: pg \\ \\ an = a1 \times q {}^{n - 1} \\ 160 = 5 \times 2 {}^{n - 1} \\ \frac{160}{5} = 2 {}^{n - 1} \\ 32 = 2 {}^{n - 1} \\ 2 {}^{5} = 2 {}^{n - 1} \\ n - 1 = 5 \\ n = 5 + 1 \\ n = 6 \\ \\ \\ \geqslant \: soma \: dos \: termos \: da \: pg \\ \\ \\ sn = \frac{a1(q {}^{n} - 1) }{q - 1} \\ \\ sn = \frac{5(2 {}^{6} - 1) }{2 - 1} \\ \\ sn = \frac{5(64 - 1)}{1} \\ \\ sn = \frac{5 \times 63}{1} \\ \\ sn = \frac{315}{1} \\ \\ sn = 315 \\ \\ \\ > < > < > < > < > < > < > > > [/tex]
