Find an equation for the nth term of a geometric sequence wh

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

A. a_n = 6 • (-4)^{n + 1}

B. a_n = 6 • 4ⁿ

C. a_n = 6 • 4^{n - 1}

D. a_n = 6 • (-4)^{n - 1}

Solution:

Here;

ar = -24 => a = -24/r

and

ar⁴ = 1536

=> (-24/r)×r⁴ = 1536

=> -24r³ = 1536

=> r³ = -64

=> r = -4

and

a = 6

As we know;

General term of G.P can be given by: an = a r^(n1)

=> an = 6×(-4)^(n-1) (D)