Mathematics
89979
28

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -12 and 768, respectively. an = 3 • (-4)n + 1 an = 3 • 4n - 1 an = 3 • (-4)n - 1 an = 3 • 4n

+2
(1) Answers
andrades

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)

Add answer