Question

the sum of the 3rd and the 7th terms of an A.P is 6 and their product is 8. find the common difference.

Answer 1

The 3rd term of an AP is a+2d and the 7th term is a+6d. So we have

the sum of 3rd term and 7th term = a+2d+a+6d = 6, or

2a+8d = 6, or

a + 4d = 3 …(1)

Their product is (a+2d)*(a+6d) = 8 …(2)

From (1), a = 3–4d. Put that in (2) to get

(a+2d)*(a+6d) = 8, or

(3–4d+2d)*(3–4d+6d) = 8, or

(3–2d)*(3+2d) = 8, or

9–4d^2 = 8, or

4d^2 = 1, or

d^2 = 1/4, or

d = 1/2.

therefore the common difference is 1/2

Answer 2

Hope this will help u and factories 2nd equation u will get answer