What number must be added to each of 4, 7, 12 so that the resulting numbers form a geometric sequence?
how about solving:
(7+x)/(4+x) = (12+x)/(7+x)
You want a constant ratio, so
(7+x)/(4+x) = (12+x)/(7+x)
x = ?
1/2
To determine what number must be added to each of 4, 7, and 12 to form a geometric sequence, we need to find the common ratio between the terms.
In a geometric sequence, each term is obtained by multiplying the preceding term by a constant value called the common ratio. Let's denote the common ratio as 'r'.
First, let's check the ratios between the consecutive terms:
- The ratio between 7 and 4 is 7/4.
- The ratio between 12 and 7 is 12/7.
For these numbers to form a geometric sequence, the ratios between each pair of consecutive terms should be equal. Therefore, we can set up the following equations:
7/4 = 12/7
To simplify the equation, we can cross-multiply:
7 * 7 = 4 * 12
49 = 48
Since 49 is not equal to 48, the numbers 4, 7, and 12 cannot form a geometric sequence.
Hence, we cannot determine a specific number to add to each term to form a geometric sequence.