Divide 32 into 4 parts which are in A.P. such that the product of extremes is to the product of means is 7:15.

 

Hi!
Here is the answer to your question.
 
Let four numbers in A.P. be a – 3d, ad, a + d and a + 3d.
(a – 3d) + (ad) + (a + d) + (a + 3d) = 32
⇒ 4a = 32
a = 8
Product of extremes = (a – 3d) (a + d) + (8 – 3d) (8 + 3d) = 64 – 9d2
Product of means = (ad) (a + d) = (8 – d) (8 + d) = 64 – d2
 
Product of extremes: product of means = 7:15  (Given)
 
When a = 8 and d = 2
a – 3d = 8 – 3 × 2 = 8 – 6 = 2
ad = 8 – 2 = 6
a + d = 8 + 2 = 10
a + 3d = 8 + 3 × 2 = 8 + 6 = 14
 
When a = 8, d = –2
a – 3d = 8 – 3 × (–2) = 8 + 6 = 14
ad = 8 – (–2) = 8 + 2 = 10
a + d = 8 – 2 = 6
a + 3d = 8 + 3 × (–2) = 8 – 6 = 2
 
∴ The four numbers are 2, 6, 10 and 14.
 
Cheers!

  • 138

Why did you select (a-3d) (a-d) (a+d) (a+3d) 

  • 58
What are you looking for?