Question

Calcule a soma dos 30 primeiros termos da Pg (-3,6,-12,24...)

Answer 1

I) Razão:

a(n) = a(1) . $q^{n-1}$

a(2) = a(1) . $q^{2-1}$

a(2) = a(1) . q

6 = -3 . q

q = 6/-3

q = -2

II) Soma dos termos:

S(n) = [a1 . ($q^{n}$ - 1)]/(q - 1)

S(30) = [-3 . (-2³⁰ - 1)]/(-2 - 1)

S(30) = [-3 . (1 073 741 824 - 1)]/-3

S(30) = (-3 . 1 073 741 823)/-3

S(30) = 1 073 741 823 = 1,073741823 . 10⁹