Question

1) verifique se as sequencias abaixo sao p.g's :
A ( a1,a2,a3,a4, a5, a6) tal que an=3x2^n-1, com n natural não nulo e n <6

Answer 1

$a_n=3\cdot2^{n-1}$

$a_1=3\cdot2^{1-1}=3\cdot2^{0}=3\cdot1=3$

$a_2=3\cdot2^{2-1}=3\cdot2^{1}=3\cdot2=6$

$a_3=3\cdot2^{3-1}=3\cdot2^2=3\cdot4=12$
$\dots$
$a_6=3\cdot2^{6-1}=3\cdot2^{5}=3\cdot12=96$

$\dfrac{a_2}{a_1}=\dfrac{6}{3}=2$

$\dfrac{a_3}{a_2}=\dfrac{12}{6}=2$
$\dots$
$\dfrac{a_6}{a_5}=\dfrac{96}{48}=2$

Logo é uma $\text{PG}$ com $a_1=3$ e $q=2$.

$\text{PG}(3,6,12,24,48,96)$