Question

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

Answer 1

Hi,

`a_(10)=a_0+10*r\\ a_7=a_0+7*r\\ a_(10)-a_7=3\ \Rightarrow 126-21=3r\ \Rightarrow r=35\\ a_7=a_0+7*r\ \Rightarrow 21=a_0+7*35\\ \Rightarrow a_0=-224\\ \Rightarrow a_1=-224+35\\ \boxed{a_1=-189}`