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

Geometric sequences are like:
a , a*r, a*r*r, a*r*r*r so on..
\[G _{5} = G _{2}*r ^{3}\] Then
\[r ^{3} = G _{5}/G _{2} = 768/-12 = -64 \rightarrow r = -4\]
\[-12 = G _{2} = r*G _{1} = r*a = -4*a \rightarrow a=3\]
So our constant is 3
then nth term would be\[G _{n} = a*r ^{n} = 3*(-4)^{n}\]

Answer 2

Here are my choices:

an = 3 • (-4)n + 1

an = 3 • 4n - 1

an = 3 • (-4)n - 1

an = 3 • 4n

Answer 3

Those answers are wrong :/

Answer 4

Those are my options...

Answer 5

Sorry, its my bad. the general term for geometric series is:\[G _{n} = a*r ^{n-1}\]
Because the first term is not a*r but a. So power of r should be 0 for n=1.
\[G _{n} = 3*(-4)^{n-1}\]

Answer 6

Thank You !