Question

Qual o termo da pg (729,2 430,8 100,...) é igual a 1000 000

Answer 1

$PG=(729,2 430,8 100,...)$

$a_{1} =729$

$q= \dfrac{2430}{729} = \dfrac{2430:243}{729:243} = \dfrac{10}{3}$

$a_{n} =1000000$

$a_{n} = a_{1} . q^{n-1}$

$1000000 = 729 . ( \dfrac{10}{3} )^{n-1}$

$( \dfrac{10}{3} )^{n-1} =\dfrac{1000000}{729}$

$( \dfrac{10}{3} )^{n-1} =\dfrac{10^{6} }{ 3^{6} }$

$( \dfrac{10}{3} )^{n-1} =( \dfrac{10}{3} )^{6}$

$n-1=6$

$n=6+1$

$n=7$

$Resposta:\text{o n\'umero 1000000 \'e o 7\º termo da PG.}$