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

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c