Find an equation for the nth term of a geometric sequence where the second and fifth terms are -24 and 1536, respectively.

Term of rank n in a G.P: a₅ = arⁿ⁻¹

a₂ = a₁.r²⁻¹ = a₁.r = - 24
a₅ = a₁.r⁵⁻¹ = a₁.r₄ = 1536 ↔ a₁.r x r³ = 1536, but  a₁.r = - 24

then: (-24) x r³ = 1536
r³ = (1536)/(-24) and r³ = - 64³ and r = ∛- 64 = r and r = -4

If r = -4 then a₁ =6 and the equation becomes :

a₅ =a₁r⁴  or a₅ =6(-4)⁴