Question

If 64, 27 and 36 are the Pth, Qth and Rth terms of a G.P, then P + 2Q is equal to

(a) R 

(b) 2R 

(c) 3R 

(d) 4R

Answer 1

(c) 3R

Let a and r be the first term and common ratio respectively of the given G.P. 

Pth term of G.P = ar^{P – 1} = 64 = 26             ...(i) 

Qth term of G.P = ar^{Q – 1} = 27 = 33           ...(ii) 

Rth term of G.P = ar^{R – 1} = 36 = 2² . 3²      ...(iii) 

Now from (i), 2 = \(a^\frac{1}{6}\) \(r^{\frac{P-1}{6}}\)                   ...(iv) 

From (ii), 3 = \(a^\frac{1}{3}\) \(r^{\frac{Q-1}{3}}\)                        ...(v) 

From (iii), 2.3 = \(a^\frac{1}{2}\) \(r^{\frac{R-1}{2}}\)                    ...(vi) 

∴ From (iv), (v) and (vi) we have

⇒ P + 2Q – 3 = 3R – 3 

⇒ P + 2Q = 3R.