Após os cálculos  chegamos ao resultado da soma dos 4 termos da PG.

[tex]\large \text {$\Rightarrow ~S4 = 19600 $}\\\\\\[/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} $}\\\\\large \text {$ 16807 = a1 ~. ~7^{4 - 1} $}\\\\\large \text {$16807= a1 ~. ~7^3 $}\\\\\large \text {$16807= a1 ~. ~343 $}\\\\\large \text {$343a1= 16807 $}\\\\\large \text {$a1 =\dfrac{16807}{343} $}\\\\\\\large \text {$a1 = 49 $}\\\\[/tex]

Soma dos quatro termos da PG.

[tex]\large \text {$Sn = \dfrac{a1 ~\cdot~( q^n) }{q - 1} $}\\\\\\\large \text {$ S4 = \dfrac{49 ~\cdot~( 7^4) -1 }{7 - 1} $}\\\\\\\large \text {$ S4 = \dfrac{49 ~\cdot~(2401 - 1) }{6} $}\\\\\\\large \text {$ S4 = \dfrac{49 ~\cdot~( 2400 ) }{6} $}\\\\\\\large \text {$ S4 = \dfrac{ 117600}{6} $}\\\\\\\large \text {$S4 = 19600 $}\\\\\\[/tex]

===

Para saber mais:

https://brainly.com.br/tarefa/49772510

https://brainly.com.br/tarefa/51212515

https://brainly.com.br/tarefa/29260869