Arecursive rule for a geometric sequence is a1=8; an=34an−1. what is the explicit rule for this sequence? enter your answer in the box. an=

ANSWER

The explicit rule is,



EXPLANATION

The recursive rule for the sequence is given as,



Where,



Let us find the next term so that we can use it to find the common ratio.

We put

into the formula to obtain,



This implies that,



This will give us









The common ratio is




This reduces to



The explicit rule of the sequence is given by



We substitute the values to obtain,