Resposta:
O primeiro termo é 7.
Explicação passo a passo:
n = 6
q = 5
an = 21.875
an = a1 . q⁽ⁿ⁻¹⁾
21.875 = a1 . 5⁽⁶⁻¹⁾
21.875 = a1 . 5⁵
21.875 = a1 . 3.125
a1 = 21.875/3.125
a1 = 7
O Valor do primeiro termo da PG.
[tex]\large\text{$\Rightarrow ~ a1 =7$}\\\\[/tex]
O valor da soma dos 6 termos da PG.
[tex]\large\text{$~\Rightarrow S6 =27342$}\\\\[/tex]
[tex]\Large\text{$ Progress\tilde{a}o ~Geom\acute{e}trica $}[/tex]
Encontrar o valor do termo a1 ( Primeiro termo da PG )
[tex]\large\text{$an = a1 ~. ~q^{n - 1} $}\\\\\\\large\text{$21.875 = a1 ~. ~5^{6 - 1} $}\\\\\\\large\text{$21.875 = a1 ~. ~5^{5} $}\\\\\\\large\text{$21.875 = a1 ~. ~3125 $}\\\\\\\large\text{$\dfrac{21875}{3125}= a1 $}\\\\\\\large\text{$a1 = 7 $}\\\\[/tex]
Encontrar o valor da soma dos seis primeiros termos da PG.
[tex]\large\text{$ Sn = \dfrac{a1 ~\cdot~( q^6 - 1) }{q - 1}$}\\\\\\\large\text{$ S6 = \dfrac{7 ~\cdot~( 5^6 - 1) }{5 - 1}$}\\\\\\\large\text{$ S6 = \dfrac{7 ~\cdot~(15625 - 1) }{4}$}\\\\\\\large\text{$ S6 = \dfrac{7 ~\cdot~(15624) }{4}$}\\\\\\\large\text{$ S6 = \dfrac{109368 }{4}$}\\\\\\\large\text{$ S6 =27342$}\\\\\\[/tex]
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Para saber mais:
https://brainly.com.br/tarefa/48629556
https://brainly.com.br/tarefa/51203261
https://brainly.com.br/tarefa/51220509
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Lista de comentários
Resposta:
O primeiro termo é 7.
Explicação passo a passo:
n = 6
q = 5
an = 21.875
an = a1 . q⁽ⁿ⁻¹⁾
21.875 = a1 . 5⁽⁶⁻¹⁾
21.875 = a1 . 5⁵
21.875 = a1 . 3.125
a1 = 21.875/3.125
a1 = 7
O Valor do primeiro termo da PG.
[tex]\large\text{$\Rightarrow ~ a1 =7$}\\\\[/tex]
O valor da soma dos 6 termos da PG.
[tex]\large\text{$~\Rightarrow S6 =27342$}\\\\[/tex]
[tex]\Large\text{$ Progress\tilde{a}o ~Geom\acute{e}trica $}[/tex]
Encontrar o valor do termo a1 ( Primeiro termo da PG )
[tex]\large\text{$an = a1 ~. ~q^{n - 1} $}\\\\\\\large\text{$21.875 = a1 ~. ~5^{6 - 1} $}\\\\\\\large\text{$21.875 = a1 ~. ~5^{5} $}\\\\\\\large\text{$21.875 = a1 ~. ~3125 $}\\\\\\\large\text{$\dfrac{21875}{3125}= a1 $}\\\\\\\large\text{$a1 = 7 $}\\\\[/tex]
Encontrar o valor da soma dos seis primeiros termos da PG.
[tex]\large\text{$ Sn = \dfrac{a1 ~\cdot~( q^6 - 1) }{q - 1}$}\\\\\\\large\text{$ S6 = \dfrac{7 ~\cdot~( 5^6 - 1) }{5 - 1}$}\\\\\\\large\text{$ S6 = \dfrac{7 ~\cdot~(15625 - 1) }{4}$}\\\\\\\large\text{$ S6 = \dfrac{7 ~\cdot~(15624) }{4}$}\\\\\\\large\text{$ S6 = \dfrac{109368 }{4}$}\\\\\\\large\text{$ S6 =27342$}\\\\\\[/tex]
===
Para saber mais:
https://brainly.com.br/tarefa/48629556
https://brainly.com.br/tarefa/51203261
https://brainly.com.br/tarefa/51220509