Question

EMERGENCY PLEASE HELP REALLY HARD!

The first and fourth terms of a geometric sequence are shown.

−2,___  , ___,  128

What are the second and third terms of this geometric sequence?

Answer 1

geometric sequence nth term:
tₙ = t₁ · (r)ⁿ⁻¹

t₁ = -2
t₄ = 128 (4th term)

formula for 4th term:

t₄ = -2 · (r)⁴⁻¹ = -2· (r)³

since t₄ = 128

128 = -2(r)³
(r)³ = -64
r = ∛-64
r = -4


so second term is
t₂ = -2· (-4)²⁻¹ = 8

third term is
t₃ = -2 · (-4)³⁻¹ = -32