Question

Calcule o 20° termo da pg(1/2,-1,2...)
respondam por favor!!!

Answer 1

$PG=(\frac{1}{2},-1,2,...)$

$a_{1}=\frac{1}{2}$

$q=\frac{a_{2}}{a_{1}}=\frac{-1}{\frac{1}{2}}=-1.2=-2$

$n=20$

$a_{20}=?$

$a_{n}=a_{1}.q^{n-1}\\\\a_{20}=\frac{1}{2} .(-2)^{20-1}\\\\a_{20}=\frac{1}{2} .(-2)^{19}\\\\a_{20}=\frac{(-2)^{19}}{2}\\\\a_{20}=-\frac{2^{19}}{2}\\\\a_{20}=2^{18}$