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Answer:
For check any equation are in AP we use find different between (a2-a1)=(a3-a2).
when u check AP in (lm+mn+nl)
firstly select (a1=lm), (a2=mn), (a3=nl)
find different (a2-a1)=(a3-a2)............ (1)
put values of a1,a2&a3 in (1)
(mn-lm)=(nl-mn)
m (n-l)=n(l-m)
similarly for l,m,n
d= (m-l)=(n-m)