for the given A.P
5,9,13,...
First term (a)=5
common difference (d) = 9-5=4
Let Tn=2012
a +(n-1) d=2012
5 +(n-1) 4=2012
(n-1) 4=2012-5
(n-1)4=2007
n-1=501.75
n=1+501.75
n=502.75 -- - - - - -> which is not possible.
No.of terms can never in fraction.
Hence, 2012 is not a term of given A.P