Paragraph: The sixth term of an AP is 2 and its common difference is greater than 1 . Question: What is the common difference of the AP so that the product of the first, fourth and fifth terms is greatest?

Step-by-step solution

Let first term = a & common difference = x aligned & a +5 x =2 a =2-5 x & Let P = T ₁ T ₄ T ₅ & P = a ( a +3 x )( a +4 x ) & P =(2-5 x )(2-5 x +3 x )(2-5 x +4 x ) & P =-10 x ^3+34 x ^2-32 x +8 & d p d x =0 15 x ^2-34 x +16=0 & (5 x -8)(3 x -2)=0 & x = 8 5 , [ x= 2 3 1 ] aligned