What is the 6th term of the geometric sequence where a1 = -4,096 and a4 = 64? A. -1 B. 4 C. 1 D. -4?

2 Answers

  • Let r be the common ratio of the geometric sequence.

    a₁ = -4096

    a₄ = 64

    -4096 × r³ = 64

    r³ = -64/4096

    r³ = -1/64

    r = -1/4

    a₆ = a₁ r⁵

    a₆ = -4096 × (-1/4)⁵

    a₆ = 4

    …… The answer: B. 4

  • a_4 = a_1 * r^(4 – 1)

    64 = -4096r^3

    -1/64 = r^3

    r = -1/4

    a_6 = a_4 * (-1/4)^(6 – 4)

    a_6 = 64 * 1/16 = 4

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