Is it arithmetic or geometric, and solve for n ( basically what is the formula and the sequence derived? )
256, 192, =7

It is geometric with common ratio 0.75 .

The explicit formula for the sequence is .

The 7th term is which is 45.5625 .

Step-by-step explanation:

It is arithmetic if you can add/subtract the same number to get from term to the term after.  In arithmetic sequence, the number you can add to get from term to term after is called the common difference. It is called common difference because it is the same number over and over.  

It is geometric if term divided previous term is the same number each time.  This is called a common ratio.  

Let's test to see if it is arithmetic.

If it is arithmetic, all of the following will have the same difference:

192-256=?

144-192=?

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192-256=-64

144-192=-48

These aren't the same number.  The sequence is not arithmetic.

Let's test to see if is geometric.

If it is geometric, all of the following will have the same ratio:

192/256=?

144/192=?

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192/256=3/4 (or .75)

144/192=3/4 (or .75)

These are the same number.  The sequence has a common ratio and is therefore geometric.

The explicit form for the equation of a geometric sequence is:

where is the first term and is the common ratio.

We have while .

The explicit form is:

The 7th term can be found by replacing with 7. Like so:

Putting right hand side into calculator reveals the 7th term is: