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# Given an A.P. whose terms are all positive integers . The sum its first nine terms is greater than 200 and less than 220 . If the second term in it is 12 , then its $\;4^{th}\;$ term is :

$(a)\;8\qquad(b)\;16\qquad(c)\;20\qquad(d)\;24$

The conditions are
a+d=12

200<9/2(2a+8d)<220

===>      92/27<d<112/27

But d has to be a integer hence d =4 , a =8

Gives a+3d=20