Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 36 and 2304, respectively.

Step-by-step explanation:

we know that

In a Geometric Sequence each term is found by multiplying the previous term by a constant, called the common ratio (r)

In this problem we have

Remember that

-----> -----> equation A

Substitute the values of a_5 and a_2 and solve for r

Find the value of a_1 in equation A

therefore

The explicit rule for the nth term is

substitute

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.