If the pth, qth and rth terms of an A.P are in GP, then the common rat

1.	If the pth, qth and rth terms of an A.P are in GP, then the common ratio of the G.P is(a) p + q/r + q(b) r - q/q - p(c) p - r/p - q(d) None of these
Answer» Correct option (b) r – q/q – p Explanation: T_p , T_q, T_r are in G.P ⇒ T_q/T_p = T_r/T_q ⇒ T_q/T_p - 1 = T_r/T_q - 1 ⇒ T_q/T_p/T_p = T_r/T_q /T_q ∴ T_q/T_p= T_r - T_q/T_q - T_p ⇒ T_q/T_p = (A (r –1)D) – (A (q – 1)D)/(A (q –1)D) – (A (p – 1)D) = r - q/q - p

If the pth, qth and rth terms of an A.P are in GP, then the common ratio of the G.P is(a) p + q/r + q(b) r - q/q - p(c) p - r/p - q(d) None of these

Answer»

Correct option (b) r – q/q – p

Explanation:

T_p , T_q, T_r are in G.P

⇒ T_q/T_p = T_r/T_q ⇒ T_q/T_p - 1 = T_r/T_q - 1

⇒ T_q/T_p/T_p = T_r/T_q /T_q

∴ T_q/T_p= T_r - T_q/T_q - T_p

⇒ T_q/T_p = (A (r –1)D) – (A (q – 1)D)/(A (q –1)D) – (A (p – 1)D)

= r - q/q - p