Answer:
[tex]\large\boxed{a_n=10-12n}[/tex]
Step-by-step explanation:
It's an arithmetic sequence.
[tex]-14-(-2)=-14+2=-12\\-26-(-14)=-26+14=-12\\-38-(-26)=-38+26=-12[/tex]
The difference is constant.
The explicit formula of an arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
Substitute:
[tex]a_1=-2,\ d=-12[/tex]
[tex]a_n=-2+(n-1)(-12)[/tex] use distributive property
[tex]a_n=-2-12n+12\\\\a_n=(-2+12)-12n\\\\a_n=10-12n[/tex]
