Question

determine a soma dos termo da p.g 1,3,9....,729

Answer 1

Boa tarde

PG

u1 = 1
u2 = 3
q = u2/u1 = 3

termo geral
un = u1*q^(n - 1)
729 = 1*3^(n - 1)
3^6 = 3^(n - 1)
n = 7 termos

soma
Sn = u1*(q^n - 1)/(q - 1)
Sn = 1"(3^7 - 1)/(3 - 1)
Sn = 1093 

Answer 2

An = 729

a₁ = 1

q = a₂ / a₁

q = 3/1

q = 3

n = ?

An = a₁ * qⁿ⁻¹

729 = 1 * 3ⁿ⁻¹

3ⁿ⁻¹ = 729 / 1

3ⁿ⁻¹ = 729

3ⁿ⁻¹ = 3⁶

n - 1 = 6

n = 1 + 6  

n = 7

Sn = a₁ * (qⁿ - 1) / q - 1

S₇ = 1 * (3⁷ - 1) / 3 - 1

S₇ = 2187 - 1 / 2

S₇ = 2186 / 2

S₇ = 1 093