Question

A sequence of numbers begins with 12 and progresses geometrically. Each number is the previous number divided by 2. Which value can be used as the common ratio in an explicit formula that represents the sequence? 2 6 12

Answer 1

First term =12

As written  Each number is the previous number divided by 2.

Second number =12÷2=6

Third term = 6÷2=3

Fourth term = 3÷2=3/2

So, the geometric series is =12 +6+3+3/2+3/4+3/8+3/16+...

Common ratio=$\frac{2nd term}{1st term}=\frac{3rd term}{2nd term}=...$

                   =$\frac{6}{12}=\frac{3}{6}=\frac{1}{2}$

The value which can be used as the common ratio in an explicit formula that represents the sequence 12 +6+3+3/2+3/4+3/8+3/16+...... is 2.