Consider the given geometric sequence,
[tex]150,120,96,76.8,\ldots\ldots\ldots[/tex]Here, the first term (a) and common ratio (r) are,
[tex]\begin{gathered} a=150 \\ r=\frac{120}{150}=0.8 \end{gathered}[/tex]Consider that the sum of an infinite geometric sequence is given by,
[tex]S=\frac{a}{1-r}[/tex]Substitute the values and simplify,
[tex]\begin{gathered} S=\frac{150}{1-0.8} \\ S=\frac{150}{0.2} \\ S=750 \end{gathered}[/tex]Thus, the sum of the given infinite geometric sequence is 750 .
