Răspuns:
Explicație pas cu pas:
progresie geometrica
a) b₁ = 1 ; q = 3 ; n = 4 ; b₄ = ? ; S₄ = ?
b₄ = b₁·q³ = 1·3³ = > b₄ = 27
S₄ = b₁+b₂+b₃+b₄
S₄ = b₁+b₁q+b₁q²+b₁q³= 1+3+9+27 = > S₄ = 40
b) b₁ = 2 ; q = -1 ; n = 5 ; b₅ = ? S₅ = ?
b₅ = b₁·q₄ = 2·(-1)⁴ = > b₅ = 2
b₂ = b₁q = -2 ; b₃ = b₂q = 2 ; b₄ = b₃q = -2
S₅ = 2-2+2-2+2 = > S₅ = 2
c) b₁ = 4 ; q = 1/2 ; bₙ = 1/8 ; n = ? Sₙ = ?
b₂ = b₁q = 4·1/2 = 2 ; b₃ = b₂q = 2·1/2 = 1
b₄ = b₃q = 1/2 ; b₅ = b₄q = 1/2 · 1/2 = 1/4
b₆ = b₅q = 1/4 · 1/2 = 1/8 => n = 6
S₆ = 4+2+1+⁴⁾1/2+²⁾1/4+1/8 = ⁸⁾7 + 7/8 => S₆ = 63/8
d) b₁ = 1 ; n = 8 ; b₈ = -128 ; q = ? S₈ = ?
b₈ = b₁q⁷ => q⁷ = b₈/b₁ = -128 = -2⁷ => q = -2
b₁ = 1 ; b₂ = -2 ; b₃ = 4 ; b₄ = -8 ; b₅ = 16 ;
b₆ = -32 ; b₇ = 64 ; b₈ = -128
S₈ = 1-2+4-8+16-32+64-128 = -1-4-16-64 = > S₈ = -85
e) q = 1/3 ; bₙ = 1/81 ; n = 4 => b₄ = 1/81 ; b₁ = ? ; S₄ = ?
b₃ = b₄/q = 1/81 : 1/3 = 3/81 = 1/27
b₂ = b₃/q = 1/27 : 1/3 = 3/27 = 1/9
b₁ = b₂/q = 1/9 : 1/3 = 3/9 = 1/3
b₁ = 1/3
S₄ = ²⁷⁾1/3 + ⁹⁾1/9 + ³⁾1/27 + 1/81 = (27+9+3+1)/81 => S₄ = 40/81
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