Question

18) Write the explicit And recursive formulas for the sequence 10, 15, 22.5, 33.75... Then, find the 24" term

of the sequence.
Recursive:
Explicit
24th Term:

Answer 1

• See below

Explanation:

Given sequence:

• 10, 15, 22.5, 33.75...

This is a GP as subsequent terms increase by 1.5 times.

The first term is:

• a₁ = 10

Common ratio is:

• r = 1.5

The recursive formula:

• a₁ = 10, aₙ = 1.5*aₙ₋₁

The explicit formula:

• aₙ = a₁*rⁿ⁻¹ ⇒
• aₙ = 10*1.5ⁿ⁻¹

The 24th term is:

• a₂₄ = 10*1.5²³