If n arithmetic means are inserted between two sets of numbers a , 2 b and 2 a , b , where a , b ∈ R . Suppose that m th arithmetic mean between these two sets of numbers is same, then the ratio a :b

Question

If n arithmetic means are inserted between two sets of numbers a , 2 b and 2 a , b , where a , b ∈ R . Suppose that m th arithmetic mean between these two sets of numbers is same, then the ratio a :b equals

TestHub · Accepted Answer

Let A 1 ​ , A 2 ​ … .. A n ​ be airthmetric means between a and 2 b , then A m ​ = a + m ( n + 1 2 b − a ​ ) \ Again, let B 1 ​ , B 2 ​ …… .. B n ​ be arithmetic means Between 2a and b then B m ​ = 2 a + m ( n + 1 b − 2 a ​ ) Now , A m ​ = B m ​ ⇒ a + m ( n + 1 2 b − a ​ ) = 2 a + m ( n + 1 b − 2 a ​ ) ⇒ m ( n + 1 b + a ​ ) = a ⇒ b a ​ = n − m + 1 m ​

Mathematics - Sequence & Series Question with Solution | TestHub

Options:

Doubts & Discussion