Question

Determine o número de termos da PG (81, 27, 9, ..., 1/9).

Answer 1

$> \: resolucao \\ \\ \geqslant \: progressao \: \: geometrica \\ \\ q = \frac{a2}{a1} = \frac{27}{81} = \frac{1}{3} \\ \\ = = = = = = = = = = \\ \\ > \: numero \: de \: termos \: da \: pg$

$an = a1 \times q {}^{n - 1} \\ \frac{1}{9} = 81 \times ( \frac{1}{3} ) {}^{n - 1} \\ \frac{ \frac{1}{9} }{81} = ( \frac{1}{3} ) {}^{n - 1} \\ \frac{1}{9} \times \frac{1}{81} = ( \frac{1}{3} ) {}^{n - 1} \\ \frac{1}{729} = ( \frac{1}{3} ) {}^{n - 1} \\ ( \frac{1}{3} ) {}^{6} = ( \frac{1}{3} ) {}^{n - 1} \\ n - 1 = 6 \\ n = 6 + 1 \\ n = 7$

$resposta \: > \: pg \: de \: 7 \: termos \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant$