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16 December, 16:42

What is the recursive formula for this geometric sequence? 4, - 12, 36, - 108, ...

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  1. 16 December, 16:54
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    aₙ = 4 (-1) ⁿ⁻¹ (3) ⁿ⁻¹

    Step-by-step explanation:

    The formula for the nth term of a geometric sequence is

    aₙ = a₁rⁿ⁻¹

    We can get the value for r by dividing aₙ by aₙ₋₁.

    a₄/a₃ = - 108/36

    a₄/a₃ = - 3

    r = - 3

    aₙ = 4 (-3) ⁿ⁻¹

    aₙ = 4 (-1) ⁿ⁻¹ (3) ⁿ⁻¹

    The (-1) ⁿ⁻¹ term makes even-numbered terms negative.
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