Option C.
Step-by-step explanation:
The given expression is ![\sum_{r=1}^{r=3}[4\times (\frac{1}{2})^{(r-1)}]](/tpl/images/0235/3119/8fc21.png)
We have to find the sum of 3 terms of the sequence formed.
The given sequence is a geometric sequence.
Explicit formula for this sequence is in the form of
![T_{n}=ar^{n-1}](/tpl/images/0235/3119/999d2.png)
In the given formula first term a = 4
and common ratio r = ![\frac{1}{2}](/tpl/images/0235/3119/9cdae.png)
Sum of a geometric sequence is represented by the expression,
![S_{n}=\frac{a(1-r^{n})}{1-r}](/tpl/images/0235/3119/59714.png)
![S_{3}=\frac{4(1-\frac{1}{2})^{3}}{(1-\frac{1}{2})}](/tpl/images/0235/3119/b410f.png)
![S_{3}=\frac{4(1-\frac{1}{8})}{(1-\frac{1}{2})}](/tpl/images/0235/3119/75e08.png)
![S_{3}=\frac{4(\frac{7}{8})}{\frac{1}{2} }](/tpl/images/0235/3119/e3f1d.png)
![S_{3}=7](/tpl/images/0235/3119/efcbb.png)
Therefore, Option C is the answer.