Question

Calcule o décimo nono (19) termo da P.G. Sendo a1=1024 e q= 1/2

Answer 1

.
$a_n=a_{19} \\ a_1=1024 \\ n=19 \\ q= \frac{1}{2} \\ \\ a_n=a_1.q^{n-1} \\ \\ a_{19}=1024.( \frac{1}{2} )^{19-1} \\ \\ a_{19}=2^{10}.2^{-18} \\ \\ a_{19}=2^{10-18} \\ \\ a_{19}=2^{-8} \\ \\ a_{19}= \frac{1}{256}$

Answer 2

$a_1=1024 \\ a_{19}=? \\ n=19 \\ q=0,5 \\ \\ a_n=a_1.q^{n-1} \\ \\ a_{19}=1024. (\frac{1}{2}) ^{(19-1)} \\ \\ a_{19}=2^{10}. (\frac{1}{2})^{18} \\ \\ a_{19}=2^{10}.2^{-18}=2^{-8} =(\frac{1}{2})^{8}=\frac{1}{256}$