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

Nth term is given by

Step-by-step explanation:

For a geometric progression we have expression for nth term

where a is first term and r is common ratio.

Here the second and fifth terms are -12 and 768.

That is

           a₂ = ar²⁻¹ = ar = -12

           a₅ = ar⁵⁻¹ = ar⁴ = 768

Dividing we will get

Substituting in

          ar = -12

          a x -4 = -12

          a = 3

Nth term is given by

a

step-by-step explanation:

6e14 is the answer.