Question

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

Answer 1

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)

Answer 2

Answer: an= 1*(-2)^n-1