What is the recursive formula for this geometric sequence? 4, - 12, 36, - 108, ...

aₙ = 4 (-1) ⁿ⁻¹ (3) ⁿ⁻¹

Step-by-step explanation:

The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

We can get the value for r by dividing aₙ by aₙ₋₁.

a₄/a₃ = - 108/36

a₄/a₃ = - 3

r = - 3

aₙ = 4 (-3) ⁿ⁻¹

aₙ = 4 (-1) ⁿ⁻¹ (3) ⁿ⁻¹

The (-1) ⁿ⁻¹ term makes even-numbered terms negative.