# Three integers are in the ratio 2:3:8. If 4 is added to the middle number, the resulting number is the second term of a geometric progression of which the other two integers are the first and third terms. How do you find the three integers?

##### 1 Answer

Nov 25, 2015

See explanation...

#### Explanation:

If the first term is

#2x, 3x+4, 8x#

The middle of three terms of a geometric sequence is equal to the geometric mean of the preceding and following terms, so:

#3x+4 = +-sqrt(2x * 8x) = +-sqrt(16 x^2) = +-4x#

If

The geometric sequence is

If

Out of curiosity let's look at this alternative non-integer solution:

#2x = -8/7#

#3x+4 = -12/7+4 = 16/7#

#8x = -32/7#

So the common ratio of this geometric sequence is