Question

If a,b,c are ina.p. and p is a.m.b/w a and b ,q is a.m. b/w b and c;show that b is the a.m. b/w p and q.

Answer 1

Answer:

Step-by-step explanation:

a, b and c are in arithmetic progression.

p is arithmetic mean between a and b.

q is arithmetic mean between b and c.

Hence a, p, b, q and c are in arithmetic progression

let d be the common difference of arithmetic progression

then p+d = b ...................(1)

and q - d = b ..................(2)

by adding (1) and (2), we get p+q = 2b

=> b = p+q/2

i.e. b is the arithmetic mean between p and q.