Misalkan X1, X2, X3, … , X22 adalah barisan aritmetika yang hasil penjumlahan dari semua suku-sukunya adalah 2024. Diketahui A = x1 + x3 + ⋯ + x21 dan B= x2 + x4 + ⋯ + x22 dengan A∶B = 11 ∶ 12.Tentukan selisih nilai suku terbesar dan suku keempat dari barisan aritmetika tersebut.
Answer (3)
The answer would most likely be (D) Primordial.
However, (C) Avant-garde, is completely legit too I suppose.
Personally I would choose (D) as my answer as it seems to make the most sense.
The answer to the question is (A) antebellum, which refers to the period before the Civil War when Southern cotton plantations depended on British textile companies. During this era, cotton became the most significant cash crop for the South, driving its economy and creating strong economic ties with Britain. This relationship was crucial for both parties, especially as the Civil War approached.
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Jawaban:1. Jumlah deret aritmetika:- Jumlah semua suku (S₂)₂ = 2024- Rumus jumlah deret aritmetika: Sₙ = n/2 × (a₁ + aₙ)- Maka, 2024 = 22/2 * (x₁ + x₂₂) => 2024 = 11 * (x₁ + x₂₂)- (x₁ + x₂₂) = 2024 / 11 = 1842. Hubungan A dan B:- A = x₁ + x₃ + ... + x₂₁ (jumlah 11 suku ganjil)- B = x₂ + x₄ + ... + x₂₂ (jumlah 11 suku genap)- A : B = 11 : 12 => A = (11/12)B- A + B = S₂₂ = 2024- (11/12)B + B = 2024 => (23/12)B = 2024 => B = (12/23) × 2024 = 1056- A = 2024 - 1056 = 9683. Gunakan rumus jumlah suku:- A = 11/2 × (x₁ + x₂₁) = 968 => (x₁ + x₂₁) = 968 × 2 / 11 = 176- B = 11/2 × (x₂ + x₂₂) = 1056 => (x₂ + x₂₂) = 1056 × 2 / 11 = 1924. Cari beda (b):- (x₂ + x₂₂) - (x₁ + x₂₁) = 192 - 176- (x₂ - x₁) + (x₂₂ - x₂₁) = 16- b + b = 16- 2b = 16 => b = 85. Cari selisih suku terbesar dan suku keempat:- Suku terbesar = x₂₂- Suku keempat = x₄- Selisih = x₂₂ - x₄ = (x₁ + 21b) - (x₁ + 3b) = 18b = 18 × 8 = 144 maka, selisih nilai suku terbesar dan suku keempat yaitu 144.
