Question

If one geometric mean G and two arithmetic means p and q be inserted between two number, then G² is equal to –

• A. (3p – q) (3q – p)
• B. (2p – q) (2q – p)
• C. (4p – q) (4q – p)
• D. None of these

Answer 1

Answer: (B)

(2p – q) (2q – p)

Answer 2

Let the two numbers be a and b, then

G = $\sqrt{ab}$ or G² = ab

Also, p and q are two A.M.s between a and b.

\ a, p, q, b are in A.P.

\ p – a = q – p and q – p = b – q

\ a = 2p – q and b = 2q – p

\ G² = ab = (2p – q) (2q – p).