Respuesta :
7 (option A)
Explanation:[tex]\begin{gathered} a_1\text{ = 4} \\ a_3\text{ = 1} \\ r\text{ = 1/2} \\ r\text{ is less than 1 here} \end{gathered}[/tex][tex]\begin{gathered} \text{Sum of geometric series:} \\ s_n\text{ = }\frac{a(1-r^n)}{1-r^{}} \\ for\text{ }when\text{ r is less than 1} \end{gathered}[/tex][tex]\begin{gathered} \text{nth term of a geometric seqeunce:} \\ a_n=a_1r^{\mleft\{n-1\mright\}} \\ n\text{ =3} \\ a_3\text{ = }4(\frac{1}{2})^{3-1} \\ a_3\text{ = }4(\frac{1}{2})^2 \\ a_3\text{ = }4(\frac{1}{4}) \\ a_3\text{ = }1 \end{gathered}[/tex][tex]\begin{gathered} s_3=\text{ }\frac{4(1-(\frac{1}{2})^3_{})}{1-(\frac{1}{2})} \\ s_3=\text{ }\frac{4(1-(\frac{1}{8})}{1-(\frac{1}{2})^{}} \end{gathered}[/tex][tex]\begin{gathered} s_3=\text{ }\frac{4(\frac{8-1}{8})}{\frac{2-1}{2}}\text{ = }\frac{4(\frac{7}{8})}{\frac{1}{2}} \\ s_3=\frac{\frac{7}{2}}{\frac{1}{2}}\text{ = }\frac{7}{2}\div\frac{1}{2} \\ s_3=\text{ }\frac{7}{2}\times\frac{2}{1} \\ s_3=\text{ 7 (option A)} \end{gathered}[/tex]