Question

Determine a soma dos termos da P.G (1,3,3^2,...3^9)
URGENTE ​

Answer 1

Resposta:

Explicação passo a passo:

Answer 2

$\largeA ~soma ~dos ~10 ~termos ~da ~PG ~ \Rightarrow ~ S10 = 29524$

                                $\Large Progress\tilde{a}o ~Geom\acute{e}trica$

Encontrar a razão da PG.

$q = \dfrac{a2}{a1} \\\\\\q = \dfrac{3}{1} \\\\\\q = 3$

Encontrar o número de termos da PG

$an = a1 ~. ~q^{n - 1}\\\\3^9 = 1 ~. ~3^{n - 1}\\\\3^9 ~. ~1 =3^{n - 1}\\\\3^9~ =3^{n - 1}\\\\9 = n-1\\\\n = 9 + 1\\\\n = 10$

Soma dos 10 termos da PG

$Sn = \dfrac{a1 ~\cdot~( q^n - 1) }{q - 1}\\\\\\S10 = \dfrac{1 ~\cdot~( 3^{10} - 1) }{3 - 1}\\\\\\S10 = \dfrac{1 ~\cdot~(59049 - 1) }{2}\\\\\\S10 = \dfrac{1 ~\cdot~59048 }{2}\\\\\\S10 = \dfrac{59048 }{2}\\\\\\S10 = 29524$

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