write the ap whose second term is 13 and the difference of the 4th term from the 8th term is 16.

Let the first term and the common difference of the given A.P. be a and d respectively.

Then,

Second term (a2) = a + d

Fourth term (a4) = a + 3d

Eighth term (a8) = a + 7d

Given : a8 - a4 = 16

a + 7d - (a + 3d) = 16

a + 7d - a - 3d = 16

⇒ 4d = 16

d = 16/4 = 4

Also 

a2 = 13

a + d = 13

a + 4 = 13

a = 13 - 4 = 9

Hence, the required A.P. is 9, 13, 17, 21, .....

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