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.

Question

Philoid · Accepted Answer

Let first term of GP be a and common ratio be r

As n^th term of GP is given as –

T_n = arⁿ ^{– 1}

∴ T₄ = ar^{4 – 1} = ar³

Similarly T₁₀ = ar⁹

And T₁₆ = ar¹⁵

∴ x = ar³, y = ar⁹ & z = ar¹⁵

Clearly we observed that x, y, z have a common ratio.

∴ x,y,z are in GP with common ratio r⁶.Hence proved.