Question

Four terms in AP have sum 28. Product of the extreme terms and that of middle terms are in ratio 5:6 .find the largest term

Answer 1

Answer:

The largest term is 10

Step-by-step explanation:

Let the AP with four terms be

a - 3d, a - d, a + d, a + 3d

By the given conditions,

a - 3d + a - d + a + d + a + 3d = 28

or, 4a = 28

or, a = 7

and (a - 3d) (a + 3d) : (a - d) (a + d) = 5 : 6

or, (a² - 9d²) / (a² - d²) = 5 / 6

or, 6 (a² - 9d²) = 5 (a² - d²)

or, 6a² - 54d² = 5a² - 5d²

or, 49d² = a²

or, 49d² = 49 , since a = 7

or, d² = 1

or, d = ± 1

When a = 7, d = 1, the AP be

4, 6, 8, 10

When a = 7, d = - 1, the AP be

10, 8, 6, 4

Therefore the largest term is 10