Find an equation for the nth term of a geometric sequence where the second and fifth terms are - 2 and 16, respectively.

Hello:

the nth term of a geometric sequence is:

Un = Up * r^ (n-p). r is the common ratio

for : p=5 and n = 2

U5 = U2 * r^3

16 = - 2 r^3

r^3 = - 8

but : - 8 = (-2) ^3

so : r = - 2

Un = U2 * r^ (n-2)

Un = - 2 * (-2) ^ (n-2) = (-2) ^ (n-2+1)

the nth term of a geometric sequenceis : Un = (-2) ^ (n-1)