Let a and b be two distinct positive real numbers. Let 11 th term of a GP, whose first term is a and third term is b , is equal to p th term of another GP, whose first term is a and fifth term is b . Then p is equal to

Step-by-step solution

Given, 1 s t G P ⇒ First term = a , a 3 = b ⇒ a r 2 = b ⇒ r 2 = b a ⇒ a 10 = a r 10 = a b a 5 . . . i 2 n d G P ⇒ First term = a , a 5 = b ⇒ a R 4 = b . . . i i ⇒ a p = a R p - 1 ⇒ a p = a b a 1 4 p - 1 . . . i i Now, using the given condition of p t h term we get, ⇒ a b a 5 = a b a p - 1 4 ⇒ b a 5 = b a p - 1 4 ⇒ 5 = p - 1 4 ⇒ p = 21