The sum of 4 consqutive terms in an A P is 32 and the ratio of the product of the first and the last term of the product of two middle terms is 7:15 find th numbers?

Four consecutive numbers are 2, 6, 10 and 14

Step-by-step explanation:

15 (a² - 9d²) = 7 (a² - d²)

15a² - 135d² = 7a² - 7d²

15a² - 7a² = 135d² - 7d²

8a² = 128d²

Putting the value of a = 8 in above we get.

8 (8) ² = 128d²

128d² = 512

d² = 512/128

d² = 4

d = 2

So, the four consecutive numbers are

8 - (3*2)

8 - 6 = 2

8 - 2 = 6

8 + 2 = 10

8 + (3*2)

8 + 6 = 14