Question

If a,A,b are in AP prove that A=a+b÷2​

Answer 1

Answer:  

Given : a,b,c are in AP then prove that (a-c)^{2}=4(a-b)(b-c)

Let,

a=a_{1},b=a_{1} +d and c=a_{1} +2d  where d is common different

Now,

LHS:-

(a-c)^{2}

=(a_{1} -a_{1}-2d)^{2}

=(-2d)^{2}

=4d^{2}

RHS:-

4(a-b)(b-c)

=4(a_{1}- a_{1}-d)(a_{1}+d-a_{1} -2d)

=4(-d)(-d)

=4d^{2}

∴ LHS=RHS