Question

I need help with the question above. I took a pic.

Answer 1

`S=(12)/(5)`

Explanation:

The common ratio of the following sequence is:

`((9)/(16))/((3)/(2))=(3)/(8)`

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:

`S=(a_1)/(1-r)`

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:

`\begin{gathered} S=((3)/(2))/(1-(3)/(8)) \\ S=((3)/(2))/((5)/(8)) \\ S=(24)/(10)=(12)/(5) \end{gathered}`