Final answer:
To find three numbers in A.P. whose sum is 21 and product is 280, we set up equations for the sum and product of an arithmetic sequence. The middle term is found to be 7, and solving gives us the three terms: 4, 7, and 10.
Step-by-step explanation:
The question asks us to find three numbers in an arithmetic progression (A.P.) such that their sum is 21 and their product is 280. Let's denote the first term of the A.P. as a, the common difference as d, and thus the three terms are a, a+d, and a+2d. Since their sum is 21, we can write the equation as:
- a + (a + d) + (a + 2d) = 21
From this equation, we can simplify to 3a + 3d = 21, which simplifies further to a + d = 7. This means that the middle term, a+d, is 7. Since the terms are in A.P., 7 is also the second term of the sequence. The product of the three terms is:
Knowing the middle term (a+d = 7), we can substitute into the product equation to find the other two terms. With some calculations, we find the three terms that satisfy both conditions are 4, 7, and 10 with the common difference d being 3.