Question

Dada a progressão geométrica, calcule o termo pedido:

Answer 1

a) 2 . $3^{9}$ = 39366
b) -3 . $2^{12}$ = -12288
c) 4 . $(-2)^{9}$ = -2048
d) 12 . $2^{-8}$
e) -3 . $5^{5}$ = -9375

Answer 2

a) $(2,6,18,\dots)~~~~~~~~a_{10}=?$

$r=\dfrac{6}{2}~~\Rightarrow~~r=3$

$a_n=a_1\cdot q^{n-1}~~~\Rightarrow~~a_{10}=a_1\cdot q^{9}$

$a_{10}=2\cdot3^{9}~~\Rightarrow~~a_{10}=2\cdot19.683~~\Rightarrow~~a_{10}=39~366$


b) $(-3,-6,-12,\dots)~~~~~~~~a_{13}=?$

$r=\dfrac{-6}{-3}~~\Rightarrow~~r=2$

$a_{13}=a_1\cdot r^{12}~~\Rightarrow~~a_{13}=(-3)\cdot2^{12}$

$a_{13}=(-3)\cdot4.096~~\Rightarrow~~a_{13}=-12.288$


c) $(4,-8,16,\dots)~~~~~~a_{10}=?$

$r=\dfrac{-8}{4}~~\Rightarrow~~r=-2$

$a_{10}=a_1\cdot q^{9}~~\Rightarrow~~a_{10}=4\cdot(-2)^{9}$

$a_{10}=4\cdot-512~~\Rightarrow~~a_{10}=-2.048$


d) $(12,6,3\dots)~~~~~~a_9=?$

$r=\dfrac{6}{12}~~\Rightarrow~~r=\dfrac{1}{2}$

$a_9=a_1\cdot q^{8}~~\Rightarrow~~a_9=12\cdot\left(\dfrac{1}{2}\right)^{8}$


$a_9=12\cdot\dfrac{1}{256}~~~\Rightarrow~~a_9=\dfrac{12}{256}~~\Rightarrow~~a_9=\dfrac{3}{64}$


e) $(-3,-15,-75,\dots)~~~~~~a_6=?$

$r=\dfrac{-15}{-3}~~~\Rightarrow~~r=5$

$a_6=a_1\cdot q^{5}~~\Rightarrow~~a_6=(-3)\cdot5^5~~\Rightarrow~~a_6=(-3)\cdot3.125$

$a_6=-9.375$