Question

Numa p. G. Tem-se a1 = 3 e a8 = 384. Calcule: a) a razão da pg; b) o terceiro termo da pg. *

Answer 1

$> \: resolucao \\ \\ \geqslant \: progressao \: geometrica \\ \\ a1 = 3 \\ an = 384 \\ n = 8 \\ \\ = = = = = = = = = = = = = \\ \\ a \: ) \: a \: razao \: da \: pg \\ \\ an = a1 \times q {}^{n - 1} \\ 384 = 3 \times q {}^{8 - 1} \\ 384 = 3 \times q {}^{7} \\ \frac{384}{3} = q {}^{7} \\ 128 = q {}^{7} \\ 2 {}^{7} = q {}^{7} \\ q = 2 \\ \\ = = = = = = = = = = = \\ \\ b \: ) \: o \: terceiro \: termo \: da \: pg \\ \\ an = a1 \times q {}^{n - 1} \\ an = 3 \times 2 {}^{3 - 1} \\ an = 3 \times 2 {}^{2} \\ an = 3 \times 4 \\ an = 12 \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant$