if a,b,c are in Arithmetic progression andGeometic progression then condition for A.P = G.P

Hello student,
please find answer toyour 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