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CGP EDU Academic Team
Published on: August 13, 2026
If 'a' is the A.M. of 'b' and 'c' and the two geometric means are G 1 and G 2 , then prove that 
= 2abc
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Sol. 'a' is the A.M. of 'b' and 'c'.
∴ a = 
⇒ b + c = 2a ....(i)
b,G 1 ,G 2 ,c are in G.P. with common ratio r = 
∴ G 1 = br = 
= c 1/3 b 2/3 and
G 2 = br 2 = 
= b 1/3 c 2/3
⇒ 
= b 2 c and 
= bc 2
⇒ 
= b 2 c + bc 2 ⇒ 
= bc(b + c)
⇒ 
= 2abc
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