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!

Answer 1

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