Question

prove that the product of the 2nd and 3rd term of an ap exceeds the product of the 1st and 4th by twice the square of the difference between the 1st and 2nd

Answer 1

Let the terms be a,b,c and d
a=a,b=a+d(common difference),c=a+2d,d=a+3d..

To prove :(a+d)×(a+2d)=a(a^2+3ad)+2d^2

Multiply 2nd and 3rd terms
(a+d)×(a+2d)=a^2+3ad+2d^2
=a(a^2+3ad)+2d^2

LHS=RHS
HENCE PROVED.

Answer 2

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