The Arithmetic Sequence Formula:
[tex]a_n=a_1+(n-1)d[/tex]
We have:
[tex]a_8=60,\ a_{12}=48[/tex]
[tex]a_n-a_m=(n-m)d\to a_{12}-a_8=(12-8)d\\\\a_{12}-a_8=4d[/tex]
Calculate d (common difference):
[tex]4d=48-60\\4d=-12\ \ \ \ |:4\\d=-3[/tex]
Calculate 40th term:
[tex]a_{40}=a_{12}+(40-12)d=a_{12}+28d[/tex]
Substitute:
[tex]a_{40}=48+28(-3)=48-84=-36[/tex]
