Question

Dê a soma dos 9 primeiros termos da P.G (12, 24, 48)

Answer 1

$(12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 + 3072) = 6132$

Answer 2

Primeiro vamos encontrar a razão :

$\mathtt{q = A_2 \div A_1} \\ \mathtt{q = 24 \div 12} \\ \mathtt{q =2 }$

Agora aplicaremos a formula geral, para descobrir o 9º termo

$\mathtt{A_n = A_1~.~q^{n-1}} \\ \\ \mathtt{A_9 = 12~.~2^{9-1}} \\ \\ \mathtt{A_9 = 12~.~2^{8}} \\ \\ \mathtt{A_9 = 12~.~256} \\ \\ \mathtt{A_9 = 12~.~256} \\ \\ \mathtt{A_9 = 3.072}$

Agora aplicar a formula de soma de P.G:

$\mathtt{S_n = \dfrac{A_1~.~(q^n-1)}{q-1} } \\ \\ \\ \mathtt{S_9 = \dfrac{12~.~(2^9-1)}{2-1} ~~=~~\dfrac{12~.~(512-1)}{2-1}~~=~~\dfrac{12~.~511}{1}~~=~~6.132} \\ \\ \\ \boxed{\boxed{\mathtt{Resposta: 6.132}}}$