Question

Determine o 8 termo de cada uma das PGs:
(1,3,9,27,...)
(8,4,2,1,1/2,...)

Answer 1

$P.G.(1,3,9,27,...)\\\\ a_{1} =1\\ q=3\\ n=8\\ a_{n} = a_{8} =?\\\\\\ a_{n} = a_{1} *q^{n-1}\\\\\\ a_{8} = 1 *3^{8-1}\to\\\\ a_{8} = 1 *3^{7}\to\\\\ a_{8} = 1 *2187\to\\\\ a_{8} = 2187$







$P.G.(8,4,2,1,1/2,...)\\\\a_{1} =8\\ q= \frac{1}{2} \\ n=8\\ a_{n} = a_{8} =?\\\\\\ a_{n} = a_{1} *q^{n-1}\\\\\\ a_{8} = 8*\frac{1}{2}^{8-1}\\\\ a_{8} = 8*\frac{1}{2}^{7}\\\\ a_{8} = 8*\frac{1}{128}\\\\ a_{8} = \frac{8}{128}\\\\ a_{8} = \frac{1}{16}$