Misalkan 1, 2, 3, … , 22 adalah barisan aritmetika yang hasil penjumlahan dari semua suku-sukunya adalah 2024. Diketahui = 1 + 3 + ⋯ + 21 dan = 2 + 4 + ⋯ + 22 dengan ∶ = 11 ∶ 12.
Tentukan selisih nilai suku terbesar dan suku keempat dari barisan aritmetika tersebut.
Answer (4)
In the Physics definition of 'work' :
-- Pick up a book from off the table.
-- Push a crate along the floor.
-- Roll a ball up a ramp.
-- Drop a rock off a cliff into the water. (Gravity does the work in this one.)
Read the question
2. Try to solve the answer
Then write the answer down
Work in physics is defined as the product of the force applied to an object and the distance over which that force is applied. Three examples include lifting a weight, pushing a box across the floor, and moving a sled down a hill, all illustrating how work is performed when there is movement. Remember that work is only done when the object moves in the direction of the applied force.
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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.
