Question

If one geometric mean G and two airthmetic mean A1, A2 are inserted between two numbers, then (2A1 – A2) (2A2 – A1) is equal to _______

(a) 2G

(b) G

(c) G^2

(d) None of the mentioned

I had been asked this question in final exam.

My enquiry is from Arithmetic and Geometric Mean topic in division Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

The correct option is (c) G^2

Explanation: Let a and b be two numbers then, G = (ab)^1/2, A1 = (2a+b)/3, A2 = (a+2b)/3, (2A1 – A2) = a, (2A2 – A1) = b, (2A1 – A2)(2A2 – A1) = G^2.