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

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