IIT JEE , AIEEE Forum - Mathematics , Algebra - Arithematic progression........................ one really irritatin prob .......

KAB

Q2)

The first term of an AP a_1,a_2,a₃,.......... is equal to unity .

At what value of common difference is a₁ a₃+ a₃ a₂is minimum ?

Given a₁=1

Let d be the common difference.

Then a₂=1+d and a₃=1+2d

Let S=a₁ a₃+ a₃ a₂

So a₁ a₃+ a₃ a₂=1+2d+1+2d+d+2d²

or S=2d²+5d+2

So S to be minimum dS/dd=0

So 4d+5=0

or d= -5/4