Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -12 and 768, respectively.

Answer 1

Let a be first term and r be common ratio, then
tn=ar^(n-1)
-12=ar^(2-1)=ar ...(1)
768=ar^(5-1) =ar^4 ....(2)
divide (2) by (1)
\[\frac{ ar ^{4} }{ar }=\frac{ 768 }{-12 },r ^{3}=-64=\left( -4 \right)^{3},r=-4\]

Answer 2

a(-4)=-12
a=-12/-4 =3
\[tn=3\left( -4 \right)^{n-1}\]

Answer 3

It's okay, I already figured that out. Thank You :)