Answer:
[tex]S=\frac{12}{5}[/tex]
Step-by-step explanation:
The common ratio of the following sequence is:
[tex]\frac{\frac{9}{16}}{\frac{3}{2}}=\frac{3}{8}[/tex]
If the common ratio is less than 1 or greater than -1 but not 0, we can use the following expression to determine the sum of the infinite geometric series:
[tex]S=\frac{a_1}{1-r}[/tex]
Therefore, if we have a common ratio of 3/8 or 0.375 and the first term of the series is 3/2.
The sum would be:
[tex]\begin{gathered} S=\frac{\frac{3}{2}}{1-\frac{3}{8}} \\ S=\frac{\frac{3}{2}}{\frac{5}{8}} \\ S=\frac{24}{10}=\frac{12}{5} \end{gathered}[/tex]
