Answer:
B
Step-by-step explanation:
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a(1-r^{n}) }{1-r}[/tex]
where a is the first term and r the common ratio
Here a = 6144 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{3072}{6144}[/tex] = [tex]\frac{1}{2}[/tex] , then
[tex]S_{10}[/tex] = [tex]\frac{6144(1-(\frac{1}{2}) ^{10}) }{1-\frac{1}{2} }[/tex]
= [tex]\frac{6144(1-\frac{1}{1024}) }{\frac{1}{2} }[/tex]
= 12288(1 - [tex]\frac{1}{1024}[/tex] ) ← distribute
= 12288 - 12
= 12276 → B
