Question

O sexto termo de uma P.G. é igual a 12500. se a razão é igual a 5, qual é o terceiro termo?

Answer 1

$a_{6}=a_{1}*q^{5}\\a_{6}/q^{3}=(a_{1}*q^{5})/q^{3}\\a_{6}/q^{3}=a_{1}*q^{2}\\\\\boxed{\boxed{a_{6}/q^{3}=a_{3}}}$
_______________________

$a_{3}=a_{6}/q^{3}\\a_{3}=12500/5^{3}\\a_{3}=12500/125\\a_{3}=100$

Se preferir o modo mais usado:

$a_{n}=a_{1}*q^{n-1}\\a_{6}=a_{1}*q^{6-1}\\a_{6}=a_{1}*q^{5}\\12500=a_{1}*5^{5}\\12500=a_{1}*3125\\12500/3125=a_{1}\\a_{1}=4$

$a_{n}=a_{1}*q^{n-1}\\a_{3}=a_{1}*q^{3-1}\\a_{3}=a_{1}*q^{2}\\a_{3}=4*5^{2}\\a_{3}=4*25\\a_{3}=100$