Question
If two G.M.'s and one A.M. 'A' be inserted between two numbers, show that
Solution
Let a and b be two numbes, since g1 and g2 are two G.M.'s between a and b.
∴ a, , b are in G.P.
Let r be common ratio
∴
Since A is the A.M. between a and b
∴ 2A = a + b ...(i)
R.H.S. = {By using (i)}
= L.H.S.