Answer :
The formula for the sum of the first n-th term is
[tex]S_n=\frac{a_1(1-r^n)_{}}{1-r}[/tex]where a_1 is the first term, r is the common ratio and n is the nth term. In our case, we have
[tex]\begin{gathered} a_1=0.4 \\ r=0.5 \\ n=5 \end{gathered}[/tex]By substiting these values into the sum formula, we have
[tex]S_5=\frac{0.4(1-0.5^5)=}{1-0.5}[/tex]which gives
[tex]S_5=\frac{0.4(1-0.03125)}{0.5}[/tex]then, the answer is
[tex]S_5=0.775[/tex]