Question

Dê 03 exemplos de cada item (a1, an, q, n e Sn)

Answer 1

Darei 1 exemplo, os outros você cria para você treinar.

Dada a sequencia: (x, 8, 4, 2,..., $\dfrac{1}{8}$)
Determine:
$a) a_{1}$
$b) a_{6}(a_{n})$
c) q
d) n (quantidade de termos)
e) Sn

a) q = $\dfrac{a_{3}}{a_{2}}$

$q=\dfrac{4}{8}$

$q=\dfrac{1}{2}$

$a_{1}=\dfrac{a_{2}}{\dfrac{1}{2}}$

$a_{1}=\dfrac{8}{\dfrac{1}{2}}$

$a_{1}=16$

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

$a_{6}=a_{1}.q^{6-1}$

$a_{6}=16.(\dfrac{1}{2})^{5}$

$a_{6}=16.(\dfrac{1}{16})$

$a_{6}=1$

c) q = $\dfrac{a_{2}}{a_{1}}$

q=$\dfrac{8}}{16}}$

q=$\dfrac{1}{2}$

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

$\dfrac{1}{8}=16.\dfrac{1}{2}^{n-1}$

$2^{-3}=2^{4}.2^{-n+1}$

$-3=4-n+1$

$-8=-n$

$n=8$

e) Sn = $\dfrac{a_{1}.(q^{n}-1)}{q.1}$

$S_{8}=\dfrac{16.((\dfrac{1}{2})^{8}-1)}{\dfrac{1}{2}}$

$S_{8}=8.(\dfrac{1}{256})-1)$

$S_{8}=8.-\dfrac{255}{256}$

$S_{8}=-\dfrac{255}{32}$

Espero ter ajudado '-'