I've attached a picture below of the formula for a finite geometric sequence. It includes an infinite geometric sequence formula for your reference, too.
[tex]a_1 = 40[/tex]
[tex]r(ratio)= \frac{1}{2} [/tex]
[tex]n=10[/tex]
Plug in the values.
[tex]S_{10}=40*( \frac{1- \frac{1}{2}^{10} }{1- \frac{1}{2} } )[/tex]
[tex]S_{10}=40*( \frac{1- \frac{1}{1024} }{\frac{1}{2} })[/tex]
[tex]S_{10}=40*( \frac{\frac{1023}{1024} }{\frac{1}{2} })[/tex]
[tex]S_{10}=40*1.998046875[/tex]
[tex] S_{10} = 79.921875[/tex]
S₁₀ ≈ 79.92
