Question

calcule a soma dos termos da P.G. (1,3,9,...,729)

Answer 1

Oi Poliana

PG 

u1 = 1
u2 = 3

q = u2/u1 = 3

termo geral
un = u1*q^(n - 1)

729 = 1*3^(n - 1) 

3^(n - 1) = 3^6 

n - 1 = 6
n = 7 

soma
Sn = u1*(q^n - 1)/(q - 1)

S7 = 1*(3^7 - 1)/(3 - 1) 
S7 = (2187 - 1)/2 = 2186/2 = 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