C I petty sure the answer is c
ANSWER
![S_5=91\frac{10}{81}](https://tex.z-dn.net/?f=S_5%3D91%5Cfrac%7B10%7D%7B81%7D)
EXPLANATION
The sum of the first
terms of a geometric sequence is given by;
![S_n=\frac{a_1(1-r^n)}{1-r} ,-1](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Ba_1%281-r%5En%29%7D%7B1-r%7D%20%2C-1%3C%5C%3Ar%3C%5C%3A1)
Where
, is the number of terms and
is the first term.
When
, we have
, we get;
![S_5=\frac{81(1-(\frac{1}{9})^5)}{1-\frac{1}{9}}](https://tex.z-dn.net/?f=S_5%3D%5Cfrac%7B81%281-%28%5Cfrac%7B1%7D%7B9%7D%29%5E5%29%7D%7B1-%5Cfrac%7B1%7D%7B9%7D%7D)
![S_5=\frac{81(1-\frac{1}{59049})}{1-\frac{1}{9}}](https://tex.z-dn.net/?f=S_5%3D%5Cfrac%7B81%281-%5Cfrac%7B1%7D%7B59049%7D%29%7D%7B1-%5Cfrac%7B1%7D%7B9%7D%7D)
![S_5=\frac{81(\frac{59048}{59049})}{\frac{8}{9}}](https://tex.z-dn.net/?f=S_5%3D%5Cfrac%7B81%28%5Cfrac%7B59048%7D%7B59049%7D%29%7D%7B%5Cfrac%7B8%7D%7B9%7D%7D)
![S_5=\frac{7381}{81}](https://tex.z-dn.net/?f=S_5%3D%5Cfrac%7B7381%7D%7B81%7D)
![S_5=91\frac{10}{81}](https://tex.z-dn.net/?f=S_5%3D91%5Cfrac%7B10%7D%7B81%7D)
Answer:
ok so first we need to find the area of the circle inside which is a=Pi*raduis^2
a=pi*1(radius is half of diamater)
a=3.14
ok then the area of the sqare including the circle is 16 so
16-3.14=12.86
this is is aprox since the area of pi is infinite and i just used 3.14
Hope This Helps!!!