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12 March, 00:22

Explicit formula of 400, 100, 25, 25/4 and use it to find the 15th term

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  1. 12 March, 02:12
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    The 15th term is 25/16'777,216

    Step-by-step explanation:

    Aₙ = Aₙ₋₁ : 4; A₁ = 400

    A₂ = A₁ : 4 = 400 : 4 = 100

    A₃ = A₂: 4 = 100 : 4 = 25

    A₄ = A₃ : 4 = 25 : 4 = 25/4

    A₅ = A₄: 4 = 25/4 : 4 = 25/4 * 1/4 = 25/16

    A₆ = A₅: 4 = 25/16 : 4 = 25/16 * 1/4 = 25/64

    A₇ = A₆: 4 = 25/64 : 4 = 25/64 * 1/4 = 25/256

    A₈ = A₇ : 4 = 25/256 : 4 = 25/256 * 1/4 = 25/1,024

    A₉ = A₈: 4 = 25/1,024 : 4 = 25/1,024 * 1/4 = 25/4,096

    A₁₀ = A₉: 4 = 25/4,096 : 4 = 25/4,096 * 1/4 = 25/16,384

    A₁₁ = A₁₀ : 4 = 25/16,384 : 4 = 25/16,384 * 1/4 = 25/65,536

    A₁₂ = A₁₁ : 4 = 25/65,536 : 4 = 25/65,536 * 1/4 = 25/262,144

    A₁₃ = A₁₂ : 4 = 25/262,144 : 4 = 25/262,144 * 1/4 = 25/1'048,576

    A₁₄ = A₁₃ : 4 = 25/1'048,576 : 4 = 25/1'048,576 * 1/4 = 25/4'194,304

    A₁₅ = A₁₄ : 4 = 25/4'194,304 : 4 = 25/4'194,304 * 1/4 = 25/16'777,216

    The 15th term is 25/16'777,216
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