Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -12 and 768, respectively.

Answer 1

For a geometric sequence, an = ar^(n - 1)
a2 = ar^(2 - 1) = ar = -12 . . . . . . . . (1)
a5 = ar^(5 - 1) = ar^4 = 768 . . . . . . (2)
(2)/(1) = ar^4/ar = 768/-12
r^3 = -64
r = ∛(-64) = -4
From (1), ar = -12
-4a = -12
a = -12/-4 = 3

Therefore, an = 3*(-4)^(n - 1)