Consider a geometric sequence whose first term is 64 and fourth term is 125. Part A: Determine the value of the common ratio.

Question

Consider a geometric sequence whose first term is 64 and fourth term is 125.
Part A: Determine the value of the common ratio.

Part B: Write the recursive formula for this sequence.

Part C: Write the explicit formula for this sequence.

Please help!

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Ngọc Khuê 4 years 2021-07-26T09:37:14+00:00 1 Answers 16 views 0

Answers ( )

  1. yenoanh
    0
    2021-07-26T09:38:48+00:00
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    Answer:

    Given a GP where:

    • a₁ = 64
    • a₄ = 125

    Part A

    Formula for nth term:

    • aₙ = a₁rⁿ⁻¹
    • a₄ = a₁r³
    • 125 = 64r³
    • r³ = 125/64
    • r = 5/4

    Part B

    Recursive formula

    • a₁ = 64
    • aₙ = (5/4)aₙ₋₁

    Part C

    Explicit formula:

    • aₙ = 64(5/4)ⁿ⁻¹

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