. The product of three numbers in A.P. is 224, and the largest number

1.	. The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest.Find the numbers.
Answer» Let the number be a,b,c ; a be the smallest and c the greatest Given a×b×c =224& c = 7a ---- e1 We know that if a,b, c are in A.P then 2b=a+c (arthimetic mean formula)2b=a+7a (given c=7a)2b = 8ab=4a ---- e2 a×b×c= 224a× 4a × 7a =224 (from e1 and e2)28a^3 = 224a^3= 224÷28a^3= 8a^3=2^3a=2 b= 4a= 4×2= 8c=7a= 7×2= 14 The numbers are 2,8,14.

. The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest.Find the numbers.

Answer»

Let the number be a,b,c ; a be the smallest and c the greatest

Given a×b×c =224& c = 7a ---- e1

We know that if a,b, c are in A.P then 2b=a+c (arthimetic mean formula)2b=a+7a (given c=7a)2b = 8ab=4a ---- e2

a×b×c= 224a× 4a × 7a =224 (from e1 and e2)28a^3 = 224a^3= 224÷28a^3= 8a^3=2^3a=2

b= 4a= 4×2= 8c=7a= 7×2= 14

The numbers are 2,8,14.