A soma dos cinco termos da PG

[tex]\large \text {$\Rightarrow S5 = 19607 $}\\\\\\[/tex]

                           [tex]\Large\text{$ Progress\tilde{a}o ~Geom\acute{e}trica $}[/tex]

Encontrar a razão da PG.

[tex]\large \text {$an = a1 ~. ~q^{n - 1} $}\\\\\large \text {$ 16807 = 7 ~. ~q^{5 - 1} $}\\\\\large \text {$16807= 7 ~. ~q^4 $}\\\\\large \text {$7q^4 = 16807 $}\\\\\\\large \text {$q^4 =\dfrac{16807}{7} $}\\\\\\\large \text {$ q^4 = 2401 $}\\\\\large \text {$q = \sqrt[4]{2401} $}\\\\\large \text {$q = 7 $}[/tex]

Soma dos 5  termos da PG.

[tex]\large \text {$Sn = \dfrac{a1 ~\cdot~( q^n) }{q - 1} $}\\\\\\\large \text {$ S5 = \dfrac{7 ~\cdot~( 7^5) -1 }{7 - 1} $}\\\\\\\large \text {$ S5 = \dfrac{7 ~\cdot~( 16807 - 1) }{6} $}\\\\\\\large \text {$ S5 = \dfrac{7 ~\cdot~( 16806) }{6} $}\\\\\\\large \text {$ S5 = \dfrac{ 117642 }{6} $}\\\\\\\large \text {$S5 = 19607 $}\\\\\\[/tex]

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