Yours Truly answers: In a geometric progression, there are two constants whose values must be found immediately: The 1st term  a  and the common ratio  r. Usually, the first term is obvious. But, in order to find the common ratio, we must ask the following question:

In order to get the 2nd term, by what number should the 1st term be multiplied?

In the above problem, the common ratio is  2. Just to be on a safe side, multiply the 2nd term by  2  and see if the result is the 3rd term, which it is. That is why  2   is called the common ratio. So,   a = 4  and  r = 2. Now, we need three formulas:
 
(1) The nth term a_n of a geometric progression: a_n = ar^n–1
 
(2) The sum  S_n  of the first  n  terms: If  r = 1, then   S_n = na. If  r  is not  1, then

 So, the original question is answered as follows:
 
(Solution)
Let  a = 4  and  r = 2. Then, the 7th term is  a ₇ = 4· 2⁶ = 256. Also, the sum of the first 7 terms is