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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!

Answer :

Mhanifago

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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