Arithmetic Sequence Question Math?

Question

Four terms in arithmetic progression have sum of 28. Product of the extreme terms and that of the middle terms are in the ratio 5:6. Find the largest term? 

Answer 1

Let the numbers be (a- 3d), (a - d), (a + d), (a + 3d).

The difference between thenumbers is 2d.

Sum  of the numbers = 28.

∴ (a- 3d) + (a - d) + (a + d) + (a + 3d) = 28

4a = 28

a = 28/4 = 7.

Product of the extreme terms and that of the middle terms are in the ratio 5:6.

∴ (a- 3d)(a + 3d) / (a - d)(a + d) = 5/6

(a² - 9d²) / (a² - d²) = 5/6

6(a² - 9d²) = 5(a² - d²)

6a² - 54d² = 5a² - 5d²

a²  = - 5d² + 54d²

a²  = 49d²

(7d)² = a²

7d = √a²

7d = a

d = a/7 = 7/7 = 1.

Therefore the numbers are (a- 3d) = 7-3 = 4, (a - d) = 7-1= 6, (a + d) = 7+1 = 8, (a + 3d) = 7+3 = 10.

Therefore the largest number is 10.