Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are - 6 and 162, respectively.

Hello,

a (2) = - 6

a (3) = - 6*r

a (4) = - 6*r²

a (5) = - 6*r^3=162

a (5) / a (2) = r^3=162 / (-6) = - 27==>r=-3

a (1) = - 6 / (-3) = 2

a (2) = 2 * (-3)

a (3) = 2 * (-3) ²

a (4) = 2 * (-3) ^3

a (5) = 2 * (-3) ^4

a (n) = 2 * (-3) ^ (n-1)

Answer