the product of 3 numbers in a.p.is 224and largest is 7 times the smallest find the numbers
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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 = 8a
b=4a ---- e2
a×b×c= 224
a× 4a × 7a =224 (from e1 and e2)
28a^3 = 224
a^3= 224÷28
a^3= 8
a^3=2^3
a=2
b= 4a= 4×2= 8
c=7a= 7×2= 14
The numbers are 2,8,14.
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 = 8a
b=4a ---- e2
a×b×c= 224
a× 4a × 7a =224 (from e1 and e2)
28a^3 = 224
a^3= 224÷28
a^3= 8
a^3=2^3
a=2
b= 4a= 4×2= 8
c=7a= 7×2= 14
The numbers are 2,8,14.
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