Question

determine o 15° termo da PG (256,128,64,32.....)?

Answer 1

Ae manu,

sendo:

$\begin{cases}a_1=256\\ q=(a_2)/(a_1)=128/256=1/2\\ n=15~termos\\ a_{15}=?\end{cases}$

então o décimo quinto termo será..

$a_n=a_1\cdot q^{n-1}\\\\ a_{15}=256\cdot \dfrac{1}{2}^{15-1}\\\\ a_{15}=256\cdot \dfrac{1}{2} ^{14} \\\\ a_{15}=256\cdot \dfrac{1}{16.384}\\\\ a_{15}= \dfrac{256}{16.384}~~~(simplifique~por~256)\\\\\\ \Large\boxed{a_{15}= \dfrac{1}{64}}}$

.....................................
ÓTIMOS ESTUDOS ;D