Question

If a , b and c are in arithmetic progression and arithmetic mean of a , b is p and b , c is q . Prove that arithmetic mean of p and q is b .

Answer 1

$\huge\boxed{Answer}$

a , b and c are in arithmetic progression .

So , 2b = a + c ------(1)

Arithmetic mean of a & b -

(a + b)/2 = p -------(2)

Same as ,

Arithmetic mean of b & c -

(b + c)/2 = q -----(3)

Therefore :-

arithmetic mean of p & q

=> (p + q)/2

=> 1/2 (p + q)

=> 1/2 (a + 2b + c)/2

=> 1/4 (a + c + 2b)

=> 1/4 (2b + 2b)

=> 1/4 × 4b

=> b

Hence proof

Answer 2

Answer:

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