Question

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

Answer 1

`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}`

Answer 2

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