Question

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

an = 2 • 3n - 1

an = 2 • (-3)n - 1

an = 2 • 3n

an = 2 • (-3)n + 1

Answer 1

nth term of a geometric series:\[a_n=a_0r^n\]
so, we have
\[-6=a_or^2\qquad{\rm and}\qquad162=a_0r^5\]
find \(a_0\) and \(r\) using these relations.
then replace in the general term.

Answer 2

\[2.-3^{n-1}\]