(3) How many terms are there in Consider the geometric sequence .
(1) Calculate .
(2) Determine the value of if .
(3) How many terms are there in this sequence?

To determine how many terms there are in the geometric sequence , we first need to find the common ratio . The ratio is found by dividing the second term by the first term:

Now we can express the -th term of the geometric sequence using the formula:

Here, . We set and solve for :

This simplifies to:

Now we simplify :

Converting into powers of :

Equating the powers of 2 gives:

So, there are 7 terms in the sequence.

For the specific calculations requested:

(1) To calculate :

We use the formula again:

(2) To find for which :

As before, solving yields:

So, there are 7 terms in the sequence.