( a_7 = 37 ), ( a_{21} = 107 )

[ \begin{align*} a + 6d &= 37 \quad (1) \ a + 20d &= 107 \quad (2) \end{align*} ]

Subtract: [ 14d = 70 \implies d = 5 ]

From (1): [ a + 6\cdot5 = 37 \implies a + 30 = 37 \implies a = 7 ]

A.P.: ( 7, 12, 17, \ldots )

100th term: [ a_{100} = 7 + 99\cdot5 = 7 + 495 = 502 ]

Answer: A.P. is ( 7, 12, 17, \ldots ); ( a_{100} = 502 )