If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

Question

Philoid · Accepted Answer

a4 = ar3

x = ar3 …………………..(i)

a10 = ar9

y = ar9…………………..(ii)

a16 = ar15

z = ar15…………………..(iii)

(ii)  (i)

y/x = ar9/ar3 = r6 …………………(iv)

(iii)  (ii)

z/y = ar15/ar9 = r6 …………………(v)

From (iv) and (v)

y/x = z/y

y2 = xz.

∴ x, y, z are in G.P

If the 4^th, 10^th and 16^th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.