if a,b,c are in arithmetic progression and geometic progression then condition for A.P = G.P

Hello student,
please find answer to your question below
since a,b,c are in AP 2b=a+c.....(1)
as also they are in GP b²=ac.......(2)
from 1 and 2 we get ((a+c)/2)²=ac
(a+c)²=4ac
(a-c)²=0so a=c
so a=b=c is the condition for AP=GP