Final answer:
In the given proportional terms, to find the sum of the extreme terms, which are (x + 1) and (x + 14), you simply add them together resulting in a sum of 2x + 15.
Step-by-step explanation:
When provided with the terms (x + 1), (x + 2)(x + 9), and (x + 14) that are in proportion, we can set up an equation representing this relationship:
(x + 1) / (x + 2)(x + 9) = (x + 2)(x + 9) / (x + 14)
This equation represents a proportion where the first and last terms are the extremes, and the middle terms are the means. To find the sum of the extreme terms, we simplifiy the equation as follows:
(x + 1)(x + 14) = (x + 2)2(x + 9)2
We are only asked to find the sum of the extremes which is:
Sum of extremes = (x + 1) + (x + 14) = 2x + 15
The sum of the extreme terms in this proportion is therefore 2x + 15.