Resposta:

n = 9

Explicação passo a passo:

a₁ = 4

a₂ = –8

q = a₂ / a₁ = –8 / 4 = –2

Sₙ = 684

n = ??

a₁ • (qⁿ – 1) / (q – 1) = Sₙ

a₁ • (qⁿ – 1)  = Sₙ • (q – 1)

qⁿ – 1  = Sₙ • (q – 1) / a₁

qⁿ  = Sₙ • (q – 1) / a₁ + 1

(–2)ⁿ  = 684 • ((–2) – 1) / 4 + 1

(–2)ⁿ  = 684 • (–3) / 4 + 1

(–2)ⁿ  = 171 • (–3) + 1

(–2)ⁿ  = –513 + 1

(–2)ⁿ  = –512

(–2)ⁿ  = (–2)⁹

n = 9