Question

If one geometric mean G and two arithemtic means p and q be inserted between two numbers, then $G^2$ is equal to:

• A. (3p-q)(3q-p)
• B. (2p-q) (2q-p)
• C. (4p-q) (4q-p)
• D. (4p+q) (4q+p)

Answer 1

The correct option is B

(2p-q) (2q-p)

Let numbers be a & b

⟹ a,g,b in G.P. and a, p, q, b in A.P.

⟹ $g^2$ = ab & p -a=q-p=b-q

we get a = 2p - q & b=2q-p

so $g^2$ = (2p - q) (2q - p)