Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 20 and 2500, respectively.

The explicit formula of the geometric sequence is:

Step-by-step explanation:

The explicit formula is the expression where the nth term is given in terms of the first term of the sequence.

We know that the explicit formula for a geometric sequence is given by:

Here we are given:

The second and fifth terms as: 20 and 2500 respectively.

i.e.

and  

i.e.

Hence,

Also,

we have:

Hence, the explicit formula is given by: