Question

The seventh term of an arithmetic sequence is 21, and the tenth term is 126. The first term is _____..

Answer 1

Pretend that the first term is 21, and the fourth term is 126 
it's the same thing. 
126 =21 +3d 
105=3d 
d=35 
21 =a1 +6(35) 
21=a1 +210 
a1=-189

Answer 2

$a_7=21;\ a_{10}=126\\\\a_{10}-a_7=3d\\\\subtitute\\\\3d=126-21\\3d=105\ \ \ |divide\ both\ sides\ by\ 3\\d=35\\\\a_1=a_7-6d\\\\a_1=21-6\cdot35=21-210=-189\\\\Answer:\boxed{a_1=-189}$