Question

Divide 96 into 4 parts which are in Arithmetic Progression and the ratio between product of their means to product of the extremes is 15 : 7. (Using Arithmetic Progression)

Answer 1

Hi there!

Let the four consecutive numbers in AP be (a - 3d), (a - d), (a + d) and (a + 3d)

ATQ,

a-3d + a - d + a + d + a + 3d = 32

4a = 32

a = 32/4

a = 8 ---(i)

Now,

(a - 3d)(a + 3d)/(a - d)(a + d) = 7/15

15(a² - 9d²) = 7(a² - d²)

15a² - 135d² = 7a² - 7d²

15a² - 7a² = 135d² - 7d² 

8a² = 128d²

Putting the value of a = 8 in above.

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

Hence,
Four consecutive numbers are 2, 6, 10 and 14

Hooe it helps!

Cheers,
Ishaan Singh