Question

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Answer 1

Răspuns:

Explicație pas cu pas:

a) a₁ = -1 ; r = 3 ; n = 12 ; S₁₂ = ?

aₙ = a₁ + (n-1)·r

a₂ = a₁+r = -1+3 = 2

a₁₂ = -1 + 11·3 = -1+33 = 32

S₁₂ = a₁+a₂+...+a₁₂ = -1+2+5+...+32 = (-1+32)·12:2 = 31·6 = 186

b) a₁ = 100 ; r = 2 ; n = 60 ; S₆₀ = ?

a₂ = a₁+r = 100+2 = 102

a₆₀ = 100 + 59·2 = 100+118 = 218

S₆₀ = 100+102+104+...+218 = (100+218)·60:2 = 318·30 = 9540

c) a₇ = 17 ; a₂ = 2 ; n = 50 ; S₅₀ = ?

a₂ = a₁+r ; a₇ = a₁+6r => a₇-a₂ = 5r = 17-2 = 15 => r = 15:5 => r = 3

a₁ = 2-3 = -1  ; a₅₀ = a₁+49r = -1+49·3 = 146

S₅₀ = -1+2+....+146 = (-1+146)·50:2 = 145·25 = 3625

d) a₃ = -12 ; a₅ = 36 ; n = 20 ; S₂₀ = ?

a₅ = a₁+4·r ; a₃ = a₁+2·r => a₅-a₃ = 2r = 36-(-12) = 48 => r = 48:2

r = 24 ; a₁ = a₃-2·r = -12-48 = -60

a₂₀ = a₁+19·r = -60 + 19·24 = 396

S₂₀ = -60-36-12+12+.....+396

S₂₀ = (-60+396)·20:2 = 336·10 = 3360