Let the geometric sequence {an} be defined as follows: {12, 6, 3, 3 /2 , 3 /4 , 3/ 8 ,...} Find the sum of the entire sequence, S∞. A) 24 B) 240 C) 1,080 Eliminate D) 2,176,782,336

Answer:A) 24Step-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