Question

In: Math

Arithmetic progression.

If a, b, c are in A.P. and P is the A.M. between a and b, and q is the A.M. between b and c, show that b is the A.M. between p and q.

Solutions

Expert Solution

Since a,b,c are in AP

2b=a+c—(i)

P is the AM between a and b

⇒P= a+b / 2

2P= a+b —(ii)

Similarly q is the A.M. between b and c

2Q=b+c —-(iii)

On adding equations (ii) and (iii) we get

2P+ 2Q=b+c + a+b

2(P+Q)= b+ (a+c)

2(P+Q)= 2b 

2(P+Q)= 4b

(P+Q) / 2= b

 

 

b is the A.M of P & Q.

Nikhil Thakur answered 2 years ago
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