The third term of an arithmetic sequence is 21, and the eighth term is 56. the first term is

Term for an AP =  a  + (n-1)d.

The third term =  a + (3 -1)d = a + 2d = 21

The eight term =   a  + (8 - 1)d = a + 7d = 56

a + 2d = 21
-
a + 7d = 56
 
0  -5d  =  -35
 
-5d = -35

d = -35/-5

d = 7

Substitute d = 7 in a + 2d = 21

a + 2d = 21
a + 2*7 = 21
a + 14 = 21
a = 21 - 14
a = 7

The first term, a = 7.