The common ratio of the geometric progression 3, 6, 12, 24 is 2.
Understanding Geometric Progressions and Common Ratios
A geometric progression (GP) is a sequence of numbers where each term is obtained by multiplying the previous term by a constant factor. This constant factor is called the common ratio.
To find the common ratio (r) of a geometric progression, you can divide any term by its preceding term.
- Formula: r = an / an-1, where an is the nth term and an-1 is the (n-1)th term.
Calculating the Common Ratio for 3, 6, 12, 24
Let's apply this to the given sequence: 3, 6, 12, 24
- Step 1: Divide the second term (6) by the first term (3).
- r = 6 / 3 = 2
- Step 2: Divide the third term (12) by the second term (6).
- r = 12 / 6 = 2
- Step 3: Divide the fourth term (24) by the third term (12).
- r = 24 / 12 = 2
As you can see, the common ratio is consistently 2. This confirms that the sequence is indeed a geometric progression, and, according to the provided information, the common ratio, r, is 2.
