Let a, b, c, be in an A.P. If m is the A.M. between a and b; and n is the A.M. between b and c
Show that b is the arithmetic mean between m and n.
Answers
Answered by
2
Answer:
The A.M of a,b is m
m=a+b/2
The A.M of b,c is n
n=b+c/2
The A.M of a,c is b
b=a+c/2
m+n=b+c/2+a+b/2
=b+c+a+b/2
=2b+a+c/2
WKT,2b=a+c if a,b,c are in A.P
=a+c+a+c/2
=2a+2c/2
2(a+c)/2
=a+c
=2(a+c/2)
=2b
Therefore,b is the A.M of m,n
Similar questions