Example 36. Prove that the product of the 2nd and 3rd term of an APexc

1.	Example 36. Prove that the product of the 2nd and 3rd term of an APexceeds the product of the 1st and 4th by twice the square of the differenceMost Importantbetween the 1st and 2nd terms
Answer» Let the terms be a,b,c and da=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=RHSHENCE PROVED.

Example 36. Prove that the product of the 2nd and 3rd term of an APexceeds the product of the 1st and 4th by twice the square of the differenceMost Importantbetween the 1st and 2nd terms

Answer»

Let the terms be a,b,c and da=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=RHSHENCE PROVED.