Question

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

Answer 1

\[
a_n = a_1 + (n-1)d
\]So \[
a_2=-6 = a_1+(2-1)d
\]And \[
a_6 = 162=a_1 + (6-1)d
\]

Two equations and two variables \(a_1, d\). Solve to win.

Answer 2

an = 2 • 3n - 1 ?

Answer 3

@wio