Arecursive rule for a geometric sequence is a1=8; an=3/4an−1 . what is the explicit rule for this sequence?

The explicit rule for this sequence is;

Step-by-step explanation:

Given the statement: A recursive rule for a geometric sequence is

and

for n= 2;

Similarly for n = 3;

Therefore, we get a geometric sequence i.e,

Now, to find the explicit rule for this geometric sequence:

A geometric sequence states that  a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r).

It is given by: where is the first term, r s the common ratio and n is the number of terms;

In the given sequence:  ,

then, the explicit rule for this sequence is;