Answer:
10
Explanation:
The formula for calculating the sum to infinity of a GP is expressed as;
[tex]S_{\infty}=\frac{a}{1-r}[/tex]a is the first term
r is the common ratio
From the given sequence;
First-term a = 5
Common ratio r = 2.5/5 = 1.25/5 = 0.5
Substitute the given values into the formula
[tex]\begin{gathered} S_{\infty\text{ }}=\text{ }\frac{5}{1-0.5} \\ S_{\infty}=\frac{5}{0.5} \\ S_{\infty}=\text{1}0 \end{gathered}[/tex]Hence the sum to infinity of the series is 10
