Question

Determinati n daca ın progresia geometrica (bn)n≥1 avem
q = 2
bn = 96
Sn = 189

Answer 1

Răspuns:

n = 6

Explicație pas cu pas:

q = 2  ; bₙ = 96  ; Sₙ = 189

bₙ = b₁·qⁿ⁻¹  =>

96 = b₁·2ⁿ⁻¹

96 = 3·2⁵  => b₁ = 3 ; n-1 = 5 => n = 6

Sₙ = S₆ = b₁+b₂+....+b₆

b₁ = 3 ; b₂ = 6 ; b₃ = 12 ; b₄ = 24 ; b₅ = 48 ; b₆ = 96

S₆ = 3+6+12+24+48+96 = 45+144 = 189 , corect

n = 6