Question

Como calcular o 12° termo da PG?

a) (4, 8, 16, 32, ...)
b) ( - 24, -4, -2/3, ...)
c) (10, -30, 90, -270, ...)

Answer 1

Temos que, $a_n=a_1\cdot q^{n-1}$. Assim, $a_{12}=a_1\cdot q^{11}$.

a) Observemos que, $a_1=4$ e $q=\dfrac{a_2}{a_1}=\dfrac{8}{4}=2$.

Logo, $a_{12}=4\cdot2^{11}=2^2\cdot2^{11}=2^{13}=8~192$

b) Vemos que, $a_1=-24$ e $q=\dfrac{-4}{-24}=\dfrac{1}{6}$

Portanto, $a_{12}=-24\cdot\left(\dfrac{1}{6}\right)^{11}=\dfrac{-24}{6^{11}}$
 
c) Do mesmo modo, $a_1=10$ e $q=\dfrac{-30}{10}=-3$.

Assim, $a_{12}=10\cdot(-3)^{12}=10\cdot531~441=5~314~410$