Answer:
A) 24
Step-by-step explanation:
The given geometric series is {12, 6, 3, 3 /2 , 3 /4 , 3/ 8 ,...}
Each term can be represented as a product of its previous term and \[\frac{1}{2}\]
The generic term of the series can be represented as the product of the first term 12 and \[\frac{1}{2}^{n-1}\] where n is the index of the term in the series.
The sum to infinity of such a series is given by the following formula:
\[\frac{term1}{1-ratio}\]
Substituting and calculating:
\[\frac{12}{1-\frac{1}{2}}\]
=\[\frac{12}{\frac{1}{2}}\]
=12*2 = 24
