If a 1 , a 2 , a 3 … and b 1 , b 2 , b 3 … . are A.P. and a 1 = 2 , a 10 = 3 , a 1 b 1 = 1 = a 10 b 10 then a 4 b 4 is equal to

Step-by-step solution

Given, a 1 , a 2 , a 3 . . . . . . &   b 1 , b 2 , b 3 .....are in A . P Also given, a 1 = 2 ,   a 10 = 3 and a 1 b 1 = 1 = a 10 b 10 So b 1 = 1 a 1 = 1 2 and b 10 = 1 a 10 = 1 3 Now using n t h term formula we get, a 10 = a 1 + 9 d a ⇒ 3 = 2 + 9 d a ⇒ d a = 1 9 Using same formula we get, b 10 = b 1 + 9 d b ⇒ 1 3 = 1 2 + 9 d b ⇒ d b = - 1 54 Now calculating a 4 b 4 = a 1 + 3 d a b 1 + 3 d b = 2 + 3 × 1 9 1 2 + 3 × - 1 54 =   7 3 × 8 18 = 56 54 = 28 27