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Răspunsuri la întrebare
Răspuns:
1. a) a₁ = 1, r = 5
a₂ = a₁ + r => a₂ = 1 + 5 = 6
a₃ = a₂ + r => 6 + 5 = 11
a₄ = a₃ + r => 11 + 5 = 16
b) a₁ = 2, r = 1
a₂ = a₁ + r = 2 + 1 = 3
a₃ = a₂ + r = 3 + 1 = 4
a₄ = a₃ + r = 4 + 1 = 5
c) a₁ = 5, r = 3
a₂ = a₁ + r = 5 + 3 = 8
a₃ = a₂ + r = 8 + 3 = 11
a₄ = a₃ + r = 11 + 3 = 14
2. a) a₁ = 8, r = 2
a₄ = a₁ + 3r => a₄ = 8 + 3 x 2 = 8 + 6 = 14
a₉ = a₁ + 8r => a₉ = 8 + 2 x 8 = 8 + 16 = 24
a₁₄ = a₁ + 13r => a₁₄ = 8 + 13 x 2 = 8 + 26 = 34
b) a₁ = 5, r = 4
a₄ = a₁ + 3r => a₄ = 5 + 4 x 3 = 5 + 12 = 17
a₉ = a₁ + 8r => a₉ = 5 + 4 x 8 = 5 + 32 = 37
a₁₄ = a₁ + 13r => a₁₄ = 5 + 4 x 13 = 5 + 52 = 57
c) a₁ = 10, r = -2
a₄ = a₁ + 3r => a₄ = 10 + 3 x (-2) = 10 - 6 = 4
a₉ = a₁ + 8r => a₉ = 10 + 8 x (-2) = 10 - 16 = -6
a₁₄ = a₁ + 13r => a₁₄ = 10 + 13 x (-2) = 10 -26 = -16
3. a) a₁ = 2, r = 1, n = 7
Sₙ = · n
aₙ = a₁ + ( n - 1 ) · r
aₙ = 2 + ( 7 - 1 ) · 1
aₙ = 2 + 6 · 1 = 8
S₇ = ·7 = 5 · 7 = 35
b) a₁ = 3, r = 2, n = 9
aₙ = 3 + ( 9 - 1 ) · 2
aₙ = 3 + 8 · 2 = 3 + 16 = 19
S₉ = · 9 = 11 · 9 = 99
c) a₁ = 5, r = 3, n = 10
aₙ = 5 + ( 10 - 1 ) · 3
aₙ = 5 + 9 · 3 = 5 + 27 = 32
S₁₀ = · 10 = 370 : 2 = 185