Ageometric sequence is defined recursively by an = 4an-1. the 1st term of the sequence is 0.5. which of the following is the explicit formula for the nth term of the sequence?

Step-by-step explanation:

The explicit formula for the nth term of the geometric sequence is given by:

             ....[1]

As per the statement:

A geometric sequence is defined recursively by:

           ....[2]

The 1st term of the sequence is 0.5

⇒

We know that:

the recursive formula for geometric sequence is given by:

where, r is the common ratio

Compare with [2] we have;

r = 4

Substitute the values of r = 4 and in [1] we have;

Therefore, the explicit formula for the nth term of the sequence is,